J. Ambjørn - Academia.edu (original) (raw)

Papers by J. Ambjørn

Research paper thumbnail of Crossing the c=1 barrier in 2D Lorentzian quantum gravity

Physical Review D, 2000

In an extension of earlier work we investigate the behaviour of two-dimensional Lorentzian quantu... more In an extension of earlier work we investigate the behaviour of two-dimensional Lorentzian quantum gravity under coupling to a conformal field theory with c > 1. This is done by analyzing numerically a system of eight Ising models (corresponding to c = 4) coupled to dynamically triangulated Lorentzian geometries. It is known that a single Ising model couples weakly to Lorentzian quantum gravity, in the sense that the Hausdorff dimension of the ensemble of two-geometries is two (as in pure Lorentzian quantum gravity) and the matter behaviour is governed by the Onsager exponents. By increasing the amount of matter to 8 Ising models, we find that the geometry of the combined system has undergone a phase transition. The new phase is characterized by an anomalous scaling of spatial length relative to proper time at large distances, and as a consequence the Hausdorff dimension is now three. In spite of this qualitative change in the geometric sector, and a very strong interaction between matter and geometry, the critical exponents of the Ising model retain their Onsager values. This provides evidence for the conjecture that the KPZ values of the critical exponents in 2d Euclidean quantum gravity are entirely due to the presence of baby universes. Lastly, we summarize the lessons learned so far from 2d Lorentzian quantum gravity.

Research paper thumbnail of Monte Carlo studies of the IIB matrix model at large N

Journal of High Energy Physics, 2000

The low-energy effective theory of the IIB matrix model developed by H. Aoki et al. is written do... more The low-energy effective theory of the IIB matrix model developed by H. Aoki et al. is written down explicitly in terms of bosonic variables only. The effective theory is then studied by Monte Carlo simulations in order to investigate the possibility of a spontaneous breakdown of Lorentz invariance. The imaginary part of the effective action, which causes the so-called sign problem in the simulation, is dropped by hand. The extent of the eigenvalue distribution of the bosonic matrices shows a power-law large N behavior, consistent with a simple branched-polymer prediction. We observe, however, that the eigenvalue distribution becomes more and more isotropic in the ten-dimensional space-time as we increase N . This suggests that if the spontaneous breakdown of Lorentz invariance really occurs in the IIB matrix model, a crucial rôle must be played by the imaginary part of the effective action.

Research paper thumbnail of Quantum geometry and diffusion

Journal of High Energy Physics, 1998

We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral di... more We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from two. We determine the scaling properties of the quantum gravity averaged diffusion kernel.

Research paper thumbnail of Monte Carlo studies of the IIB matrix model at large N

Journal of High Energy Physics, 2000

The low-energy effective theory of the IIB matrix model developed by H. Aoki et al. is written do... more The low-energy effective theory of the IIB matrix model developed by H. Aoki et al. is written down explicitly in terms of bosonic variables only. The effective theory is then studied by Monte Carlo simulations in order to investigate the possibility of a spontaneous breakdown of Lorentz invariance. The imaginary part of the effective action, which causes the so-called sign problem in the simulation, is dropped by hand. The extent of the eigenvalue distribution of the bosonic matrices shows a power-law large N behavior, consistent with a simple branched-polymer prediction. We observe, however, that the eigenvalue distribution becomes more and more isotropic in the ten-dimensional space-time as we increase N . This suggests that if the spontaneous breakdown of Lorentz invariance really occurs in the IIB matrix model, a crucial rôle must be played by the imaginary part of the effective action.

Research paper thumbnail of The Factorization method for simulating systems with a complex action

We propose a method for Monte Carlo simulations of systems with a complex action. The method has ... more We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix theory of finite density QCD where we compare with analytic results. In this model we find non-commutativity of the limits µ → 0 and N → ∞ which could be of relevance in QCD at finite density.

Research paper thumbnail of Quantum geometry of topological gravity

Physics Letters B, 1997

We study a c = ?2 conformal eld theory coupled to two-dimensional quantum gravity by means of dyn... more We study a c = ?2 conformal eld theory coupled to two-dimensional quantum gravity by means of dynamical triangulations. We de ne the geodesic distance r on the triangulated surface with N triangles, and show that dim r d H ] = dim N ], where the fractal dimension d H = 3:58 0:04. This result lends support to the conjecture d H = ?2 1 = ?1 , where ?n is the gravitational dressing exponent of a spin-less primary eld of conformal weight (n + 1; n + 1), and it disfavors the alternative prediction d H = ?2= str . On the other hand, we nd dim l ] = dim r 2 ] with good accuracy, where l is the length of one of the boundaries of a circle with (geodesic) radius r, i.e. the length l has an anomalous dimension relative to the area of the surface. It is further shown that the spectral dimension d s = 1:980 0:014 for the ensemble of (triangulated) manifolds used. The results are derived using nite size scaling and a very e cient recursive sampling technique known previously to work well for c = ?2.

Research paper thumbnail of The factorization method for systems with a complex action. A test in Random Matrix Theory for finite density QCD

Journal of High Energy Physics, 2002

Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A n... more Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A new approach to this problem based on a factorization property of distribution functions of observables has been proposed recently. The method can be applied to any system with a complex action, and it eliminates the so-called overlap problem completely. We test the new approach in a Random Matrix Theory for finite density QCD, where we are able to reproduce the exact results for the quark number density. The achieved system size is large enough to extract the thermodynamic limit. Our results provide a clear understanding of how the expected first order phase transition is induced by the imaginary part of the action.

Research paper thumbnail of Spin-spin correlation functions of spin systems coupled to 2-d quantum gravity for 0 < c < 1

Nuclear Physics B - Proceedings Supplements, 1997

We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces coupled to Ising and ... more We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces coupled to Ising and three-states Potts model matter. By measuring spin-spin correlation functions as a function of the geodesic distance we provide substantial evidence for a diverging correlation length at βc. The corresponding scaling exponents are directly related to the KPZ exponents of the matter fields as conjectured in .

Research paper thumbnail of New perspective on matter coupling in 2D quantum gravity

Physical Review D, 1999

We provide compelling evidence that a previously introduced model of nonperturbative 2D Lorentzia... more We provide compelling evidence that a previously introduced model of nonperturbative 2D Lorentzian quantum gravity exhibits ͑two-dimensional͒ flat-space behavior when coupled to Ising spins. The evidence comes from both a high-temperature expansion and from Monte Carlo simulations of the combined gravitymatter system. This weak-coupling behavior lends further support to the conclusion that the Lorentzian model is a genuine alternative to Liouville quantum gravity in two dimensions, with a different and much ''smoother'' critical behavior. 1 Alternatively, one could embed quantum gravity in a larger, unified theory such as string theory or ͑the as yet nonexistent͒ M theory. However, these are still far from giving us any detailed information about the quantum gravity sector.

Research paper thumbnail of Complex zeros of the 2d Ising model on dynamical random lattices

Nuclear Physics B - Proceedings Supplements, 1998

We study the zeros in the complex plane of the partition function for the Ising model coupled to ... more We study the zeros in the complex plane of the partition function for the Ising model coupled to 2d quantum gravity for complex magnetic field and for complex temperature. We compute the zeros by using the exact solution coming from a two matrix model and by Monte Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional patterns in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of singularities near the critical point.

Research paper thumbnail of Abelian Gauge Fields Coupled to Simplicial Quantum Gravity

We study the coupling of Abelian gauge theories to four-dimensional simplicial quantum gravity. T... more We study the coupling of Abelian gauge theories to four-dimensional simplicial quantum gravity. The gauge fields live on dual links. This is the correct formulation if we want to compare the effect of gauge fields on geometry with similar effects studied so far for scalar fields. It shows that gauge fields couple equally weakly to geometry as scalar fields, and it offers an understanding of the relation between measure factors and Abelian gauge fields observed so-far. 1 email ambjorn@nbi.dk 2 email konstant@nbi.dk. Address after September 1st:

Research paper thumbnail of High-temperature, classical, real-time dynamics of non-abelian gauge theories as seen by a computer

Journal of High Energy Physics, 2001

We test at the electroweak scale the recently proposed elaborate theoretical scenario for real-ti... more We test at the electroweak scale the recently proposed elaborate theoretical scenario for real-time dynamics of non-abelian gauge theories at high temperature. We see no sign of the predicted behavior. This indicates that perturbative concepts like color conductivity and Landau damping might be irrelevant at temperatures corresponding to the electroweak scale.

Research paper thumbnail of Real-time dynamics of a hot Yang-Mills theory: a numerical analysis

Nuclear Physics B - Proceedings Supplements, 2002

We discuss recent results obtained from simulations of high temperature, classical, real time dyn... more We discuss recent results obtained from simulations of high temperature, classical, real time dynamics of SU (2) Yang-Mills theory at temperatures of the order of the electroweak scale. Measurements of gauge covariant and gauge invariant autocorrelations of the fields indicate that the ASY-Bödecker scenario is irrelevant at these temperatures.

Research paper thumbnail of Anti-screening of large magnetic fields by vector bosons

Physics Letters B, 1988

In the SO (3) model with massive vector bosons we show that for magnetic fields exceeding m 2/e t... more In the SO (3) model with massive vector bosons we show that for magnetic fields exceeding m 2/e there is condensation of W's. This condensation is characterized by anti-screening. Near the critical field we show that the condensate is a lattice of vortex lines.

Research paper thumbnail of World-sheet dynamics of ZZ-branes

Physics Letters B, 2007

We show how non-compact space-time (ZZ branes) emerges as a limit of compact space-time (FZZT bra... more We show how non-compact space-time (ZZ branes) emerges as a limit of compact space-time (FZZT branes) for specific ratios between the square of the boundary cosmological constant and the bulk cosmological constant in the (2, 2m−1) minimal model coupled to two-dimensional quantum gravity.

Research paper thumbnail of Search for scaling dimensions for random surfaces with c = 1

Physics Letters B, 1995

We study numerically the fractal structure of the intrinsic geometry of random surfaces coupled t... more We study numerically the fractal structure of the intrinsic geometry of random surfaces coupled to matter elds with c = 1. Using baby universe surgery it was possible to simulate randomly triangulated surfaces made of 260.000 triangles. Our results are consistent with the theoretical prediction d H = 2 + p 2 for the intrinsic Hausdor dimension.

Research paper thumbnail of Noncommutativity of the zero chemical potential limit and the thermodynamic limit in finite density systems

Physical Review D, 2004

Monte Carlo simulations of finite density systems are often plagued by the complex action problem... more Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain non-commutativity in the zero chemical potential limit and the thermodynamic limit when one tries to study such systems by reweighting techniques. This is demonstrated by explicit calculations in a Random Matrix Theory, which is thought to be a simple qualitative model for finite density QCD. The factorization method allows us to understand how the non-commutativity, which appears at the intermediate steps, cancels in the end results for physical observables.

Research paper thumbnail of On the spontaneous breakdown of Lorentz symmetry in matrix models of superstrings

Physical Review D, 2002

In string or M theories, the spontaneous breaking of 10D or 11D Lorentz symmetry is required to d... more In string or M theories, the spontaneous breaking of 10D or 11D Lorentz symmetry is required to describe our space-time. A direct approach to this issue is provided by the type IIB matrix model. We study its 4D version, which corresponds to the zero volume limit of 4D super SU(N) Yang-Mills theory. Based on the moment of inertia as a criterion, spontaneous symmetry breaking ͑SSB͒ seems to occur, so that only one extended direction remains, as first observed by Bialas and Burda et al. However, using Wilson loops as probes of space-time we do not observe any sign of SSB in Monte Carlo simulations where N is as large as 48. This agrees with an earlier observation that the phase of the fermionic integral, which is absent in the 4D model, should play a crucial role if SSB of Lorentz symmetry really occurs in the 10D type IIB matrix model. 1 Dimensionally reduced Yang-Mills theories were first studied in Refs. ͓4͔.

Research paper thumbnail of Three-dimensional simplicial quantum gravity coupled to Ising matter

Nuclear Physics B - Proceedings Supplements, 1993

... Modern Physics Letters A (MPLA). Particles and Fields; Gravitation; Cosmology and Nuclear Phy... more ... Modern Physics Letters A (MPLA). Particles and Fields; Gravitation; Cosmology and Nuclear Physics. ...

Research paper thumbnail of ELECTROWEAK MAGNETISM: THEORY AND APPLICATIONS

International Journal of Modern Physics A, 1990

... Black hole instability induced by a magnetic field. Physics Letters B 706:1, 94-99. [CrossRef... more ... Black hole instability induced by a magnetic field. Physics Letters B 706:1, 94-99. [CrossRef] 3. Julien Garaud, Mikhail S. Volkov. 2010. ... Superconductivity of QCD vacuum in strong magnetic field. Physical Review D 82:8. . [CrossRef] 5. Julien Garaud, Mikhail S. Volkov. 2010. ...

Research paper thumbnail of Crossing the c=1 barrier in 2D Lorentzian quantum gravity

Physical Review D, 2000

In an extension of earlier work we investigate the behaviour of two-dimensional Lorentzian quantu... more In an extension of earlier work we investigate the behaviour of two-dimensional Lorentzian quantum gravity under coupling to a conformal field theory with c > 1. This is done by analyzing numerically a system of eight Ising models (corresponding to c = 4) coupled to dynamically triangulated Lorentzian geometries. It is known that a single Ising model couples weakly to Lorentzian quantum gravity, in the sense that the Hausdorff dimension of the ensemble of two-geometries is two (as in pure Lorentzian quantum gravity) and the matter behaviour is governed by the Onsager exponents. By increasing the amount of matter to 8 Ising models, we find that the geometry of the combined system has undergone a phase transition. The new phase is characterized by an anomalous scaling of spatial length relative to proper time at large distances, and as a consequence the Hausdorff dimension is now three. In spite of this qualitative change in the geometric sector, and a very strong interaction between matter and geometry, the critical exponents of the Ising model retain their Onsager values. This provides evidence for the conjecture that the KPZ values of the critical exponents in 2d Euclidean quantum gravity are entirely due to the presence of baby universes. Lastly, we summarize the lessons learned so far from 2d Lorentzian quantum gravity.

Research paper thumbnail of Monte Carlo studies of the IIB matrix model at large N

Journal of High Energy Physics, 2000

The low-energy effective theory of the IIB matrix model developed by H. Aoki et al. is written do... more The low-energy effective theory of the IIB matrix model developed by H. Aoki et al. is written down explicitly in terms of bosonic variables only. The effective theory is then studied by Monte Carlo simulations in order to investigate the possibility of a spontaneous breakdown of Lorentz invariance. The imaginary part of the effective action, which causes the so-called sign problem in the simulation, is dropped by hand. The extent of the eigenvalue distribution of the bosonic matrices shows a power-law large N behavior, consistent with a simple branched-polymer prediction. We observe, however, that the eigenvalue distribution becomes more and more isotropic in the ten-dimensional space-time as we increase N . This suggests that if the spontaneous breakdown of Lorentz invariance really occurs in the IIB matrix model, a crucial rôle must be played by the imaginary part of the effective action.

Research paper thumbnail of Quantum geometry and diffusion

Journal of High Energy Physics, 1998

We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral di... more We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from two. We determine the scaling properties of the quantum gravity averaged diffusion kernel.

Research paper thumbnail of Monte Carlo studies of the IIB matrix model at large N

Journal of High Energy Physics, 2000

The low-energy effective theory of the IIB matrix model developed by H. Aoki et al. is written do... more The low-energy effective theory of the IIB matrix model developed by H. Aoki et al. is written down explicitly in terms of bosonic variables only. The effective theory is then studied by Monte Carlo simulations in order to investigate the possibility of a spontaneous breakdown of Lorentz invariance. The imaginary part of the effective action, which causes the so-called sign problem in the simulation, is dropped by hand. The extent of the eigenvalue distribution of the bosonic matrices shows a power-law large N behavior, consistent with a simple branched-polymer prediction. We observe, however, that the eigenvalue distribution becomes more and more isotropic in the ten-dimensional space-time as we increase N . This suggests that if the spontaneous breakdown of Lorentz invariance really occurs in the IIB matrix model, a crucial rôle must be played by the imaginary part of the effective action.

Research paper thumbnail of The Factorization method for simulating systems with a complex action

We propose a method for Monte Carlo simulations of systems with a complex action. The method has ... more We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix theory of finite density QCD where we compare with analytic results. In this model we find non-commutativity of the limits µ → 0 and N → ∞ which could be of relevance in QCD at finite density.

Research paper thumbnail of Quantum geometry of topological gravity

Physics Letters B, 1997

We study a c = ?2 conformal eld theory coupled to two-dimensional quantum gravity by means of dyn... more We study a c = ?2 conformal eld theory coupled to two-dimensional quantum gravity by means of dynamical triangulations. We de ne the geodesic distance r on the triangulated surface with N triangles, and show that dim r d H ] = dim N ], where the fractal dimension d H = 3:58 0:04. This result lends support to the conjecture d H = ?2 1 = ?1 , where ?n is the gravitational dressing exponent of a spin-less primary eld of conformal weight (n + 1; n + 1), and it disfavors the alternative prediction d H = ?2= str . On the other hand, we nd dim l ] = dim r 2 ] with good accuracy, where l is the length of one of the boundaries of a circle with (geodesic) radius r, i.e. the length l has an anomalous dimension relative to the area of the surface. It is further shown that the spectral dimension d s = 1:980 0:014 for the ensemble of (triangulated) manifolds used. The results are derived using nite size scaling and a very e cient recursive sampling technique known previously to work well for c = ?2.

Research paper thumbnail of The factorization method for systems with a complex action. A test in Random Matrix Theory for finite density QCD

Journal of High Energy Physics, 2002

Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A n... more Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A new approach to this problem based on a factorization property of distribution functions of observables has been proposed recently. The method can be applied to any system with a complex action, and it eliminates the so-called overlap problem completely. We test the new approach in a Random Matrix Theory for finite density QCD, where we are able to reproduce the exact results for the quark number density. The achieved system size is large enough to extract the thermodynamic limit. Our results provide a clear understanding of how the expected first order phase transition is induced by the imaginary part of the action.

Research paper thumbnail of Spin-spin correlation functions of spin systems coupled to 2-d quantum gravity for 0 < c < 1

Nuclear Physics B - Proceedings Supplements, 1997

We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces coupled to Ising and ... more We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces coupled to Ising and three-states Potts model matter. By measuring spin-spin correlation functions as a function of the geodesic distance we provide substantial evidence for a diverging correlation length at βc. The corresponding scaling exponents are directly related to the KPZ exponents of the matter fields as conjectured in .

Research paper thumbnail of New perspective on matter coupling in 2D quantum gravity

Physical Review D, 1999

We provide compelling evidence that a previously introduced model of nonperturbative 2D Lorentzia... more We provide compelling evidence that a previously introduced model of nonperturbative 2D Lorentzian quantum gravity exhibits ͑two-dimensional͒ flat-space behavior when coupled to Ising spins. The evidence comes from both a high-temperature expansion and from Monte Carlo simulations of the combined gravitymatter system. This weak-coupling behavior lends further support to the conclusion that the Lorentzian model is a genuine alternative to Liouville quantum gravity in two dimensions, with a different and much ''smoother'' critical behavior. 1 Alternatively, one could embed quantum gravity in a larger, unified theory such as string theory or ͑the as yet nonexistent͒ M theory. However, these are still far from giving us any detailed information about the quantum gravity sector.

Research paper thumbnail of Complex zeros of the 2d Ising model on dynamical random lattices

Nuclear Physics B - Proceedings Supplements, 1998

We study the zeros in the complex plane of the partition function for the Ising model coupled to ... more We study the zeros in the complex plane of the partition function for the Ising model coupled to 2d quantum gravity for complex magnetic field and for complex temperature. We compute the zeros by using the exact solution coming from a two matrix model and by Monte Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional patterns in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of singularities near the critical point.

Research paper thumbnail of Abelian Gauge Fields Coupled to Simplicial Quantum Gravity

We study the coupling of Abelian gauge theories to four-dimensional simplicial quantum gravity. T... more We study the coupling of Abelian gauge theories to four-dimensional simplicial quantum gravity. The gauge fields live on dual links. This is the correct formulation if we want to compare the effect of gauge fields on geometry with similar effects studied so far for scalar fields. It shows that gauge fields couple equally weakly to geometry as scalar fields, and it offers an understanding of the relation between measure factors and Abelian gauge fields observed so-far. 1 email ambjorn@nbi.dk 2 email konstant@nbi.dk. Address after September 1st:

Research paper thumbnail of High-temperature, classical, real-time dynamics of non-abelian gauge theories as seen by a computer

Journal of High Energy Physics, 2001

We test at the electroweak scale the recently proposed elaborate theoretical scenario for real-ti... more We test at the electroweak scale the recently proposed elaborate theoretical scenario for real-time dynamics of non-abelian gauge theories at high temperature. We see no sign of the predicted behavior. This indicates that perturbative concepts like color conductivity and Landau damping might be irrelevant at temperatures corresponding to the electroweak scale.

Research paper thumbnail of Real-time dynamics of a hot Yang-Mills theory: a numerical analysis

Nuclear Physics B - Proceedings Supplements, 2002

We discuss recent results obtained from simulations of high temperature, classical, real time dyn... more We discuss recent results obtained from simulations of high temperature, classical, real time dynamics of SU (2) Yang-Mills theory at temperatures of the order of the electroweak scale. Measurements of gauge covariant and gauge invariant autocorrelations of the fields indicate that the ASY-Bödecker scenario is irrelevant at these temperatures.

Research paper thumbnail of Anti-screening of large magnetic fields by vector bosons

Physics Letters B, 1988

In the SO (3) model with massive vector bosons we show that for magnetic fields exceeding m 2/e t... more In the SO (3) model with massive vector bosons we show that for magnetic fields exceeding m 2/e there is condensation of W's. This condensation is characterized by anti-screening. Near the critical field we show that the condensate is a lattice of vortex lines.

Research paper thumbnail of World-sheet dynamics of ZZ-branes

Physics Letters B, 2007

We show how non-compact space-time (ZZ branes) emerges as a limit of compact space-time (FZZT bra... more We show how non-compact space-time (ZZ branes) emerges as a limit of compact space-time (FZZT branes) for specific ratios between the square of the boundary cosmological constant and the bulk cosmological constant in the (2, 2m−1) minimal model coupled to two-dimensional quantum gravity.

Research paper thumbnail of Search for scaling dimensions for random surfaces with c = 1

Physics Letters B, 1995

We study numerically the fractal structure of the intrinsic geometry of random surfaces coupled t... more We study numerically the fractal structure of the intrinsic geometry of random surfaces coupled to matter elds with c = 1. Using baby universe surgery it was possible to simulate randomly triangulated surfaces made of 260.000 triangles. Our results are consistent with the theoretical prediction d H = 2 + p 2 for the intrinsic Hausdor dimension.

Research paper thumbnail of Noncommutativity of the zero chemical potential limit and the thermodynamic limit in finite density systems

Physical Review D, 2004

Monte Carlo simulations of finite density systems are often plagued by the complex action problem... more Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain non-commutativity in the zero chemical potential limit and the thermodynamic limit when one tries to study such systems by reweighting techniques. This is demonstrated by explicit calculations in a Random Matrix Theory, which is thought to be a simple qualitative model for finite density QCD. The factorization method allows us to understand how the non-commutativity, which appears at the intermediate steps, cancels in the end results for physical observables.

Research paper thumbnail of On the spontaneous breakdown of Lorentz symmetry in matrix models of superstrings

Physical Review D, 2002

In string or M theories, the spontaneous breaking of 10D or 11D Lorentz symmetry is required to d... more In string or M theories, the spontaneous breaking of 10D or 11D Lorentz symmetry is required to describe our space-time. A direct approach to this issue is provided by the type IIB matrix model. We study its 4D version, which corresponds to the zero volume limit of 4D super SU(N) Yang-Mills theory. Based on the moment of inertia as a criterion, spontaneous symmetry breaking ͑SSB͒ seems to occur, so that only one extended direction remains, as first observed by Bialas and Burda et al. However, using Wilson loops as probes of space-time we do not observe any sign of SSB in Monte Carlo simulations where N is as large as 48. This agrees with an earlier observation that the phase of the fermionic integral, which is absent in the 4D model, should play a crucial role if SSB of Lorentz symmetry really occurs in the 10D type IIB matrix model. 1 Dimensionally reduced Yang-Mills theories were first studied in Refs. ͓4͔.

Research paper thumbnail of Three-dimensional simplicial quantum gravity coupled to Ising matter

Nuclear Physics B - Proceedings Supplements, 1993

... Modern Physics Letters A (MPLA). Particles and Fields; Gravitation; Cosmology and Nuclear Phy... more ... Modern Physics Letters A (MPLA). Particles and Fields; Gravitation; Cosmology and Nuclear Physics. ...

Research paper thumbnail of ELECTROWEAK MAGNETISM: THEORY AND APPLICATIONS

International Journal of Modern Physics A, 1990

... Black hole instability induced by a magnetic field. Physics Letters B 706:1, 94-99. [CrossRef... more ... Black hole instability induced by a magnetic field. Physics Letters B 706:1, 94-99. [CrossRef] 3. Julien Garaud, Mikhail S. Volkov. 2010. ... Superconductivity of QCD vacuum in strong magnetic field. Physical Review D 82:8. . [CrossRef] 5. Julien Garaud, Mikhail S. Volkov. 2010. ...