Niels Obers | University of Copenhagen (original) (raw)
Papers by Niels Obers
We consider the conformal gauging of non-abelian groups. In such cases there are inequivalent way... more We consider the conformal gauging of non-abelian groups. In such cases there are inequivalent ways of gauging (generalizing the axial and vector cases for abelian groups) corresponding to external automorphisms of the group. Different σ-models obtained this way correspond to the same conformal field theory. We use the method of quotients to formulate this equivalence as a new duality symmetry.
Lecture Notes in Physics, 1999
Based on our work [1], we discuss how U-duality arises as an exact symmetry of M-theory from T-du... more Based on our work [1], we discuss how U-duality arises as an exact symmetry of M-theory from T-duality and 11D diffeomorphism invariance. A set of Weyl generators are shown to realize the Weyl group of SO(d, d, Z) and E d(d) (Z), while Borel generators extend these finite groups into the full T-and U-duality groups. We discuss how the BPS states fall into various representations, and obtain duality invariant mass formulae, relevant for the computation of exact string amplitudes. The realization of U-duality symmetry in Matrix gauge theory is also considered.
Journal of High Energy Physics, 2002
Following recent advances in the local theory of current-algebraic orbifolds we present the basic... more Following recent advances in the local theory of current-algebraic orbifolds we present the basic dynamics — including the twisted KZ equations — of each twisted sector of all outer-automorphic WZW orbifolds on (2n). Physics-friendly cartesian bases are used throughout, and we are able in particular to assemble two ℤ3 triality orbifolds and three S3 triality orbifolds on (8).
We find a realization of linear electroelasticity theory in gravitational physics by uncovering a... more We find a realization of linear electroelasticity theory in gravitational physics by uncovering a new response coefficient of charged black branes, exhibiting their piezoelectric behavior. Taking charged dilatonic black strings as an example and using the blackfold approach we measure their elastic and piezolectric moduli. We also use our results to draw predictions about the equilibrium condition of charged dilatonic black rings in dimensions higher than six.
Physical Review D, 2011
We construct different neutral blackfold solutions in Anti-de Sitter and de Sitter background spa... more We construct different neutral blackfold solutions in Anti-de Sitter and de Sitter background spacetimes in the limit where the cosmological constant is taken to be much smaller than the horizon size. This includes a class of blackfolds with horizons that are products of odd-spheres times a transverse sphere, for which the thermodynamic stability is also studied. Moreover, we exhibit a specific case in which the same blackfold solution can describe different limiting black hole spacetimes therefore illustrating the geometric character of the blackfold approach. Furthermore, we show that the higher-dimensional Kerr-(Anti)-de Sitter black hole allows for ultra-spinning regimes in the same limit under consideration and demonstrate that this is correctly described by a pancaked blackfold geometry. We also give evidence for the possibility of saturating the rigidity theorem in these backgrounds.
Journal of High Energy Physics, 2012
We study the giant graviton solution as the AdS 5 × S 5 background is heated up to finite tempera... more We study the giant graviton solution as the AdS 5 × S 5 background is heated up to finite temperature. The analysis employs the thermal brane probe technique based on the blackfold approach. We focus mainly on the thermal giant graviton corresponding to a thermal D3-brane probe wrapped on an S 3 moving on the S 5 of the background at finite temperature. We find several interesting new effects, including that the thermal giant graviton has a minimal possible value for the angular momentum and correspondingly also a minimal possible radius of the S 3 . We compute the free energy of the thermal giant graviton in the low temperature regime, which potentially could be compared to that of a thermal state on the gauge theory side. Moreover, we analyze the space of solutions and stability of the thermal giant graviton and find that, in parallel with the extremal case, there are two available solutions for a given temperature and angular momentum, one stable and one unstable. In order to write down the equations of motion, action and conserved charges for the thermal giant graviton we present a slight generalization of the blackfold formalism for charged black branes. Finally, we also briefly consider the thermal giant graviton moving in the AdS 5 part.
Journal of High Energy Physics, 2013
ABSTRACT
Journal of High Energy Physics, 2001
We obtain the operator algebra of each twisted sector of all WZW orbifolds, including the general... more We obtain the operator algebra of each twisted sector of all WZW orbifolds, including the general twisted current algebra and the algebra of the twisted currents with the twisted affine primary fields. Surprisingly, the twisted right and left mover current algebras are not a priori copies of each other. Using the operator algebra we also derive world-sheet differential equations for the twisted affine primary fields of all WZW orbifolds. Finally we include ground state properties to obtain the twisted Knizhnik-Zamolodchikov equations of the WZW permutation orbifolds and the inner-
Journal of High Energy Physics, 2013
We present the first-order corrected dynamics of fluid branes carrying higher-form charge by obta... more We present the first-order corrected dynamics of fluid branes carrying higher-form charge by obtaining the general form of their equations of motion to pole-dipole order. Assuming linear response theory, we characterize the corresponding effective theory of stationary bent charged (an)isotropic fluid branes in terms of two sets of response coefficients, the Young modulus and the piezoelectric moduli. We subsequently find large classes of examples in gravity of this effective theory, by constructing stationary strained charged black brane solutions to first order in a derivative expansion. Using solution generating techniques and bent neutral black branes as a seed solution, we obtain a class of charged black brane geometries carrying smeared Maxwell charge in Einstein-Maxwell-dilaton gravity. In the specific case of ten-dimensional space-time we furthermore use T-duality to generate bent black branes with higher-form charge, including smeared D-branes of type II string theory. By subsequently measuring the bending moment and the electric dipole moment which these geometries acquire due to the strain, we uncover that their form is captured by classical electroelasticity theory. In particular, we find that the Young modulus and the piezoelectric moduli of our strained charged black brane solutions are parameterized by a total of 4 response coefficients, both for the isotropic as well as anisotropic cases.
Journal of High Energy Physics, 2012
We explore corrections in the blackfold approach, which is a worldvolume theory capturing the dyn... more We explore corrections in the blackfold approach, which is a worldvolume theory capturing the dynamics of thin black branes. The corrections probe the fine structure of the branes, going beyond the approximation in which they are infinitely thin, and account for the dipole moment of worldvolume stress-energy as well as the internal spin degrees of freedom. We show that the dipole correction is induced elastically by bending a black brane. We argue that the long-wavelength transport coefficient capturing this response is a relativistic generalization of the Young modulus of elastic materials and we compute it analytically. Using this we draw predictions for black rings in dimensions greater than six. Furthermore, we employ our corrected blackfold equations to various multi-spinning black hole configurations in the blackfold limit, finding perfect agreement with known analytic solutions.
Journal of High Energy Physics, 1997
We continue our study of heterotic/type-I duality in D < 10 dimensions. We consider the heterotic... more We continue our study of heterotic/type-I duality in D < 10 dimensions. We consider the heterotic and type-I theories compactified on tori to lower dimensions. We calculate the special ("BPS-saturated") F 4 and R 4 terms in the effective one-loop heterotic action. These terms are expected to be non-perturbatively exact for D > 4.
Journal of High Energy Physics, 2000
A detailed understanding of instanton effects for half-BPS couplings is pursued in theories with ... more A detailed understanding of instanton effects for half-BPS couplings is pursued in theories with 16 supersymmetries. In particular, we investigate the duality between heterotic string on T 4 and type IIA on K 3 at the T 4 /Z 2 orbifold point, as well as their higher and lower dimensional versions. We present a remarkably clean quantitative test of the duality at the level of F 4 couplings, by completely matching a purely one-loop heterotic amplitude to a purely tree-level type II result. The triality of SO(4, 4) and several other miracles are shown to be crucial for the duality to hold. Exact non-perturbative new results for type I', F on K 3 , M on K 3 , and IIB on K 3 are found, and the general form of D-instanton contributions in type IIA or B on T 4 /Z 2 is obtained. We also analyze the NS5-brane contributions in type II on K 3 × T 2 , and predict the value µ(N) = d|N (1/d 3 ) for the bulk contribution to the index of the NS5-brane world-volume theory on K 3 × T 2 .
Physics Reports, 1996
This is a review of irrational conformal field theory, which includes rational conformal field th... more This is a review of irrational conformal field theory, which includes rational conformal field theory as a small subspace. Central topics of the review include the Virasoro master equation, its solutions and the dynamics of irrational conformal field theory. Discussion of the dynamics includes the generalized Knizhnik-Zamolodchikov equations on the sphere, the corresponding heat-like systems on the torus and the generic world-sheet action of irrational conformal field theory. *
Physics Letters B, 1994
We consider the conformal gauging of non-abelian groups. In such cases there are inequivalent way... more We consider the conformal gauging of non-abelian groups. In such cases there are inequivalent ways of gauging (generalizing the axial and vector cases for abelian groups) corresponding to external automorphisms of the group. Different σ-models obtained this way correspond to the same conformal field theory. We use the method of quotients to formulate this equivalence as a new duality symmetry.
Physical Review D, 2013
Fluid mechanics can be formulated on dynamical surfaces of arbitrary co-dimension embedded in a b... more Fluid mechanics can be formulated on dynamical surfaces of arbitrary co-dimension embedded in a background space-time. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary fluid configurations. Motivated by this approach we show under certain conditions that a given stationary fluid configuration living on a dynamical surface of vanishing thickness and satisfying locally the first law of thermodynamics will behave like an elastic brane when the surface is subject to small deformations. These results, which are independent of the number of space-time dimensions and of the fluid arising from a gravitational dual, reveal the (electro)elastic character of (charged) black branes when considering extrinsic perturbations. arXiv:1210.5197v1 [hep-th]
Nuclear Physics B, 1998
The full U-duality symmetry of toroidally compactified M-theory can only be displayed by allowing... more The full U-duality symmetry of toroidally compactified M-theory can only be displayed by allowing non-rectangular tori with expectation values of the gauge fields.
Nuclear Physics B, 1991
An exact C-function, which is an action for the Virasoro master equation, is obtained on affine-V... more An exact C-function, which is an action for the Virasoro master equation, is obtained on affine-Virasoro space. The solutions of the master equation are fixed points of an associated flow, which obeys a C-theorem. The closed sub-flow SO(n) diag is a flow on the space of graphs, and the associated Morse polynomials are known generating functions in graph theory. The general flow also implies a method for prediction of sporadic conformal deformations. We note the resemblance of this system to the expected form of an exact renormalization group equation.
Nuclear Physics B, 1998
We compute and analyse a variety of four-derivative gravitational terms in the effective action o... more We compute and analyse a variety of four-derivative gravitational terms in the effective action of six-and four-dimensional type II string ground states with N = 4 supersymmetry. In six dimensions, we compute the relevant perturbative corrections for the type II string compactified on K3. In four dimensions we do analogous computations for several models with (4, 0) and (2, 2) supersymmetry. Such ground states are related by heterotic-type II duality or type II-type II U-duality. Perturbative computations in one member of a dual pair give a non-perturbative result in the other member. In particular, the exact CP-even R 2 coupling on the (2, 2) side reproduces the tree-level term plus NS 5-brane instanton contributions on the (4, 0) side. On the other hand, the exact CP-odd coupling yields the one-loop axionic interaction aR ∧ R together with a similar instanton sum. In a subset of models, the expected breaking of the SL(2, Z) S S-duality symmetry to a Γ(2) S subgroup is observed on the non-perturbative thresholds. Moreover, we present a duality chain that provides evidence for the existence of heterotic N = 4 models in which N = 8 supersymmetry appears at strong coupling.
International Journal of Modern Physics A, 2002
Recently the operator algebra and twisted vertex operator equations were given for each sector of... more Recently the operator algebra and twisted vertex operator equations were given for each sector of all WZW orbifolds, and a set of twisted KZ equations for the WZW permutation orbifolds were worked out as a large example. In this companion paper we report two further large examples of this development. In the first example we solve the twisted vertex operator equations in an abelian limit to obtain the twisted vertex operators and correlators of a large class of abelian orbifolds. In the second example, the twisted vertex operator equations are applied to obtain a set of twisted KZ equations for the (outer-automorphic) charge conjugation orbifold on su(n ≥ 3). †
We consider the conformal gauging of non-abelian groups. In such cases there are inequivalent way... more We consider the conformal gauging of non-abelian groups. In such cases there are inequivalent ways of gauging (generalizing the axial and vector cases for abelian groups) corresponding to external automorphisms of the group. Different σ-models obtained this way correspond to the same conformal field theory. We use the method of quotients to formulate this equivalence as a new duality symmetry.
Lecture Notes in Physics, 1999
Based on our work [1], we discuss how U-duality arises as an exact symmetry of M-theory from T-du... more Based on our work [1], we discuss how U-duality arises as an exact symmetry of M-theory from T-duality and 11D diffeomorphism invariance. A set of Weyl generators are shown to realize the Weyl group of SO(d, d, Z) and E d(d) (Z), while Borel generators extend these finite groups into the full T-and U-duality groups. We discuss how the BPS states fall into various representations, and obtain duality invariant mass formulae, relevant for the computation of exact string amplitudes. The realization of U-duality symmetry in Matrix gauge theory is also considered.
Journal of High Energy Physics, 2002
Following recent advances in the local theory of current-algebraic orbifolds we present the basic... more Following recent advances in the local theory of current-algebraic orbifolds we present the basic dynamics — including the twisted KZ equations — of each twisted sector of all outer-automorphic WZW orbifolds on (2n). Physics-friendly cartesian bases are used throughout, and we are able in particular to assemble two ℤ3 triality orbifolds and three S3 triality orbifolds on (8).
We find a realization of linear electroelasticity theory in gravitational physics by uncovering a... more We find a realization of linear electroelasticity theory in gravitational physics by uncovering a new response coefficient of charged black branes, exhibiting their piezoelectric behavior. Taking charged dilatonic black strings as an example and using the blackfold approach we measure their elastic and piezolectric moduli. We also use our results to draw predictions about the equilibrium condition of charged dilatonic black rings in dimensions higher than six.
Physical Review D, 2011
We construct different neutral blackfold solutions in Anti-de Sitter and de Sitter background spa... more We construct different neutral blackfold solutions in Anti-de Sitter and de Sitter background spacetimes in the limit where the cosmological constant is taken to be much smaller than the horizon size. This includes a class of blackfolds with horizons that are products of odd-spheres times a transverse sphere, for which the thermodynamic stability is also studied. Moreover, we exhibit a specific case in which the same blackfold solution can describe different limiting black hole spacetimes therefore illustrating the geometric character of the blackfold approach. Furthermore, we show that the higher-dimensional Kerr-(Anti)-de Sitter black hole allows for ultra-spinning regimes in the same limit under consideration and demonstrate that this is correctly described by a pancaked blackfold geometry. We also give evidence for the possibility of saturating the rigidity theorem in these backgrounds.
Journal of High Energy Physics, 2012
We study the giant graviton solution as the AdS 5 × S 5 background is heated up to finite tempera... more We study the giant graviton solution as the AdS 5 × S 5 background is heated up to finite temperature. The analysis employs the thermal brane probe technique based on the blackfold approach. We focus mainly on the thermal giant graviton corresponding to a thermal D3-brane probe wrapped on an S 3 moving on the S 5 of the background at finite temperature. We find several interesting new effects, including that the thermal giant graviton has a minimal possible value for the angular momentum and correspondingly also a minimal possible radius of the S 3 . We compute the free energy of the thermal giant graviton in the low temperature regime, which potentially could be compared to that of a thermal state on the gauge theory side. Moreover, we analyze the space of solutions and stability of the thermal giant graviton and find that, in parallel with the extremal case, there are two available solutions for a given temperature and angular momentum, one stable and one unstable. In order to write down the equations of motion, action and conserved charges for the thermal giant graviton we present a slight generalization of the blackfold formalism for charged black branes. Finally, we also briefly consider the thermal giant graviton moving in the AdS 5 part.
Journal of High Energy Physics, 2013
ABSTRACT
Journal of High Energy Physics, 2001
We obtain the operator algebra of each twisted sector of all WZW orbifolds, including the general... more We obtain the operator algebra of each twisted sector of all WZW orbifolds, including the general twisted current algebra and the algebra of the twisted currents with the twisted affine primary fields. Surprisingly, the twisted right and left mover current algebras are not a priori copies of each other. Using the operator algebra we also derive world-sheet differential equations for the twisted affine primary fields of all WZW orbifolds. Finally we include ground state properties to obtain the twisted Knizhnik-Zamolodchikov equations of the WZW permutation orbifolds and the inner-
Journal of High Energy Physics, 2013
We present the first-order corrected dynamics of fluid branes carrying higher-form charge by obta... more We present the first-order corrected dynamics of fluid branes carrying higher-form charge by obtaining the general form of their equations of motion to pole-dipole order. Assuming linear response theory, we characterize the corresponding effective theory of stationary bent charged (an)isotropic fluid branes in terms of two sets of response coefficients, the Young modulus and the piezoelectric moduli. We subsequently find large classes of examples in gravity of this effective theory, by constructing stationary strained charged black brane solutions to first order in a derivative expansion. Using solution generating techniques and bent neutral black branes as a seed solution, we obtain a class of charged black brane geometries carrying smeared Maxwell charge in Einstein-Maxwell-dilaton gravity. In the specific case of ten-dimensional space-time we furthermore use T-duality to generate bent black branes with higher-form charge, including smeared D-branes of type II string theory. By subsequently measuring the bending moment and the electric dipole moment which these geometries acquire due to the strain, we uncover that their form is captured by classical electroelasticity theory. In particular, we find that the Young modulus and the piezoelectric moduli of our strained charged black brane solutions are parameterized by a total of 4 response coefficients, both for the isotropic as well as anisotropic cases.
Journal of High Energy Physics, 2012
We explore corrections in the blackfold approach, which is a worldvolume theory capturing the dyn... more We explore corrections in the blackfold approach, which is a worldvolume theory capturing the dynamics of thin black branes. The corrections probe the fine structure of the branes, going beyond the approximation in which they are infinitely thin, and account for the dipole moment of worldvolume stress-energy as well as the internal spin degrees of freedom. We show that the dipole correction is induced elastically by bending a black brane. We argue that the long-wavelength transport coefficient capturing this response is a relativistic generalization of the Young modulus of elastic materials and we compute it analytically. Using this we draw predictions for black rings in dimensions greater than six. Furthermore, we employ our corrected blackfold equations to various multi-spinning black hole configurations in the blackfold limit, finding perfect agreement with known analytic solutions.
Journal of High Energy Physics, 1997
We continue our study of heterotic/type-I duality in D < 10 dimensions. We consider the heterotic... more We continue our study of heterotic/type-I duality in D < 10 dimensions. We consider the heterotic and type-I theories compactified on tori to lower dimensions. We calculate the special ("BPS-saturated") F 4 and R 4 terms in the effective one-loop heterotic action. These terms are expected to be non-perturbatively exact for D > 4.
Journal of High Energy Physics, 2000
A detailed understanding of instanton effects for half-BPS couplings is pursued in theories with ... more A detailed understanding of instanton effects for half-BPS couplings is pursued in theories with 16 supersymmetries. In particular, we investigate the duality between heterotic string on T 4 and type IIA on K 3 at the T 4 /Z 2 orbifold point, as well as their higher and lower dimensional versions. We present a remarkably clean quantitative test of the duality at the level of F 4 couplings, by completely matching a purely one-loop heterotic amplitude to a purely tree-level type II result. The triality of SO(4, 4) and several other miracles are shown to be crucial for the duality to hold. Exact non-perturbative new results for type I', F on K 3 , M on K 3 , and IIB on K 3 are found, and the general form of D-instanton contributions in type IIA or B on T 4 /Z 2 is obtained. We also analyze the NS5-brane contributions in type II on K 3 × T 2 , and predict the value µ(N) = d|N (1/d 3 ) for the bulk contribution to the index of the NS5-brane world-volume theory on K 3 × T 2 .
Physics Reports, 1996
This is a review of irrational conformal field theory, which includes rational conformal field th... more This is a review of irrational conformal field theory, which includes rational conformal field theory as a small subspace. Central topics of the review include the Virasoro master equation, its solutions and the dynamics of irrational conformal field theory. Discussion of the dynamics includes the generalized Knizhnik-Zamolodchikov equations on the sphere, the corresponding heat-like systems on the torus and the generic world-sheet action of irrational conformal field theory. *
Physics Letters B, 1994
We consider the conformal gauging of non-abelian groups. In such cases there are inequivalent way... more We consider the conformal gauging of non-abelian groups. In such cases there are inequivalent ways of gauging (generalizing the axial and vector cases for abelian groups) corresponding to external automorphisms of the group. Different σ-models obtained this way correspond to the same conformal field theory. We use the method of quotients to formulate this equivalence as a new duality symmetry.
Physical Review D, 2013
Fluid mechanics can be formulated on dynamical surfaces of arbitrary co-dimension embedded in a b... more Fluid mechanics can be formulated on dynamical surfaces of arbitrary co-dimension embedded in a background space-time. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary fluid configurations. Motivated by this approach we show under certain conditions that a given stationary fluid configuration living on a dynamical surface of vanishing thickness and satisfying locally the first law of thermodynamics will behave like an elastic brane when the surface is subject to small deformations. These results, which are independent of the number of space-time dimensions and of the fluid arising from a gravitational dual, reveal the (electro)elastic character of (charged) black branes when considering extrinsic perturbations. arXiv:1210.5197v1 [hep-th]
Nuclear Physics B, 1998
The full U-duality symmetry of toroidally compactified M-theory can only be displayed by allowing... more The full U-duality symmetry of toroidally compactified M-theory can only be displayed by allowing non-rectangular tori with expectation values of the gauge fields.
Nuclear Physics B, 1991
An exact C-function, which is an action for the Virasoro master equation, is obtained on affine-V... more An exact C-function, which is an action for the Virasoro master equation, is obtained on affine-Virasoro space. The solutions of the master equation are fixed points of an associated flow, which obeys a C-theorem. The closed sub-flow SO(n) diag is a flow on the space of graphs, and the associated Morse polynomials are known generating functions in graph theory. The general flow also implies a method for prediction of sporadic conformal deformations. We note the resemblance of this system to the expected form of an exact renormalization group equation.
Nuclear Physics B, 1998
We compute and analyse a variety of four-derivative gravitational terms in the effective action o... more We compute and analyse a variety of four-derivative gravitational terms in the effective action of six-and four-dimensional type II string ground states with N = 4 supersymmetry. In six dimensions, we compute the relevant perturbative corrections for the type II string compactified on K3. In four dimensions we do analogous computations for several models with (4, 0) and (2, 2) supersymmetry. Such ground states are related by heterotic-type II duality or type II-type II U-duality. Perturbative computations in one member of a dual pair give a non-perturbative result in the other member. In particular, the exact CP-even R 2 coupling on the (2, 2) side reproduces the tree-level term plus NS 5-brane instanton contributions on the (4, 0) side. On the other hand, the exact CP-odd coupling yields the one-loop axionic interaction aR ∧ R together with a similar instanton sum. In a subset of models, the expected breaking of the SL(2, Z) S S-duality symmetry to a Γ(2) S subgroup is observed on the non-perturbative thresholds. Moreover, we present a duality chain that provides evidence for the existence of heterotic N = 4 models in which N = 8 supersymmetry appears at strong coupling.
International Journal of Modern Physics A, 2002
Recently the operator algebra and twisted vertex operator equations were given for each sector of... more Recently the operator algebra and twisted vertex operator equations were given for each sector of all WZW orbifolds, and a set of twisted KZ equations for the WZW permutation orbifolds were worked out as a large example. In this companion paper we report two further large examples of this development. In the first example we solve the twisted vertex operator equations in an abelian limit to obtain the twisted vertex operators and correlators of a large class of abelian orbifolds. In the second example, the twisted vertex operator equations are applied to obtain a set of twisted KZ equations for the (outer-automorphic) charge conjugation orbifold on su(n ≥ 3). †