Christian Schubert - Academia.edu (original) (raw)
Papers by Christian Schubert
Physical Review D, 2006
In a previous paper [G. V. Dunne and C. Schubert, Phys. Rev. D 72, 105004 (2005).PRVDAQ0556-28211... more In a previous paper [G. V. Dunne and C. Schubert, Phys. Rev. D 72, 105004 (2005).PRVDAQ0556-282110.1103/PhysRevD.72.105004], it was shown that the worldline expression for the nonperturbative imaginary part of the QED effective action can be approximated by the contribution of a special closed classical path in Euclidean spacetime, known as a worldline instanton. Here we extend this formalism to compute
Quantum Theory and Symmetries - Proceedings of the 3rd International Symposium, 2004
The Euler-Heisenberg effective action in a self-dual background is remarkably simple at two-loop.... more The Euler-Heisenberg effective action in a self-dual background is remarkably simple at two-loop. This simplicity is due to the inter-relationship between self-duality, helicity and supersymmetry. Applications include two-loop helicity amplitudes, beta-functions and nonperturbative effects. The two-loop Euler-Heisenberg effective Lagrangian for QED in a self-dual background field is naturally expressed in terms of one-loop quantities. This mirrors similar behavior recently found in two-loop amplitudes in N=4 SUSY Yang-Mills theory.
In recent years, the Euler-Heisenberg Lagrangian has been shown to be a useful tool for the analy... more In recent years, the Euler-Heisenberg Lagrangian has been shown to be a useful tool for the analysis of the asymptotic growth of the N-photon amplitudes at large N. Moreover, certain results and conjectures on its imaginary part allow one, using Borel analysis, to make predictions for those amplitudes at large loop orders. Extending work by G.V. Dunne and one of
We present a scalar thick brane configuration arising in a theory of 5D gravity coupled to a self... more We present a scalar thick brane configuration arising in a theory of 5D gravity coupled to a self-interacting scalar field. We start from a classical solution of the field equations and study the physics of linear fluctuations around this background which obey a Schrödinger-like equation. We further focus our attention on a special case in which it is possible to
Journal of High Energy Physics, 2006
We obtain closed-form expressions, in terms of the Faulhaber numbers, for the weak-field expansio... more We obtain closed-form expressions, in terms of the Faulhaber numbers, for the weak-field expansion coefficients of the two-loop Euler-Heisenberg effective Lagrangians in a magnetic or electric field. This follows from the observation that the magnetic worldline Green's function has a natural expansion in terms of the Faulhaber numbers.
Theoretical and Mathematical Physics, 1997
We clarify a discrepancy between two previous calculations of the two-loop QED Euler-Heisenberg L... more We clarify a discrepancy between two previous calculations of the two-loop QED Euler-Heisenberg Lagrangian, both performed in proper-time regularization, by calculating this quantity in dimensional regularization.
Journal of High Energy Physics, 2008
The worldline formalism has in recent years emerged as a powerful tool for the computation of eff... more The worldline formalism has in recent years emerged as a powerful tool for the computation of effective actions and heat kernels. However, implementing nontrivial boundary conditions in this formalism has turned out to be a difficult problem. Recently, such a generalization was developed for the case of a scalar field on the half-space R + × R D−1 , based on an extension of the associated worldline path integral to the full R D using image charges. We present here an improved version of this formalism which allows us to write down non-recursive master formulas for the n -point contribution to the heat kernel trace of a scalar field on the half-space with Dirichlet or Neumann boundary conditions. These master formulas are suitable to computerization. We demonstrate the efficiency of the formalism by a calculation of two new heat-kernel coefficients for the half-space, a 4 and a 9/2 .
Journal of High Energy Physics, 2005
In part 1 of this series compact integral representations had been obtained for the one-loop phot... more In part 1 of this series compact integral representations had been obtained for the one-loop photon-graviton amplitude involving a charged spin 0 or spin 1/2 particle in the loop and an arbitrary constant electromagnetic field. In this sequel, we study the structure and magnitude of the various polarization components of this amplitude on-shell. Explicit expressions are obtained for a number of limiting cases. arXiv:0710.5572v1 [gr-qc]
Journal of High Energy Physics, 2002
We analyze the structure of the imaginary part of the two-loop Euler-Heisenberg QED effective Lag... more We analyze the structure of the imaginary part of the two-loop Euler-Heisenberg QED effective Lagrangian for a constant self-dual background. The novel feature of the two-loop result, compared to one-loop, is that the prefactor of each exponential (instanton) term in the imaginary part has itself an asymptotic expansion. We also perform a high-precision test of Borel summation techniques applied to the weak-field expansion, and find that the Borel dispersion relations reproduce the full prefactor of the leading imaginary contribution.
Journal of High Energy Physics, 2010
We continue an effort to obtain information on the QED perturbation series at high loop orders, a... more We continue an effort to obtain information on the QED perturbation series at high loop orders, and particularly on the issue of large cancellations inside gauge invariant classes of graphs, using the example of the l -loop N -photon amplitudes in the limit of large photons numbers and low photon energies. As was previously shown, high-order information on these amplitudes can be obtained from a nonperturbative formula, due to Affleck et al., for the imaginary part of the QED effective lagrangian in a constant field. The procedure uses Borel analysis and leads, under some plausible assumptions, to a number of nontrivial predictions already at the three-loop level. Their direct verification would require a calculation of this 'Euler-Heisenberg lagrangian' at three-loops, which seems presently out of reach. Motivated by previous work by Dunne and Krasnansky on Euler-Heisenberg lagrangians in various dimensions, in the present work we initiate a new line of attack on this problem by deriving and proving the analogous predictions in the simpler setting of 1+1 dimensional QED. In the first part of this series, we obtain a generalization of the formula of Affleck et al. to this case, and show that, for both Scalar and Spinor QED, it correctly predicts the leading asymptotic behaviour of the weak field expansion coefficients of the two loop Euler-Heisenberg lagrangians.
Physics Letters B, 1998
We consider the one-loop e ective action due to a spinor loop coupled to an abelian vector and ax... more We consider the one-loop e ective action due to a spinor loop coupled to an abelian vector and axial vector eld background. After rewriting this e ective action in terms of an auxiliary non-abelian gauge connection, we use the De Witt expansion to analyze both its anomalous and non-anomalous content. The same transformation allows us to obtain a novel worldline path integral representation for this e ective action which avoids the usual separation into the real and imaginary parts of the Euclidean e ective action, as well as the introduction of auxiliary dimensions. 11.15Bt email: (1) TMLEAFS@APMATHS.UWO.CA/ (2) SCHUBERT@LAPP.IN2P3.FR
Physics Letters B, 1995
We construct the world-line action for a Dirac particle coupled to a classical scalar or pseudo-s... more We construct the world-line action for a Dirac particle coupled to a classical scalar or pseudo-scalar background field. This action can be used to compute loop diagrams and the effective action in the Yukawa model using the world-line path-integral formalism for spinning particles.
Physics Letters B, 1999
The superconformal Ward identities combined with N s 2 harmonic analyticity are used to evaluate ... more The superconformal Ward identities combined with N s 2 harmonic analyticity are used to evaluate two-loop four-point correlation functions of gauge-invariant operators in D s 4, N s 4 supersymmetric Yang-Mills theory in terms of the well-known one-loop box integral. The result is confirmed by a direct numerical computation. q 1999 Elsevier Science B.V. All rights reserved.
Physics Letters B, 2000
Ž It is shown that certain extremal correlators in four-dimensional N s 2 superconformal field th... more Ž It is shown that certain extremal correlators in four-dimensional N s 2 superconformal field theories including N s 4 . super-Yang-Mills as a special case have a free-field functional form. It is further argued that the coupling constant dependence receives no correction beyond the lowest order. These results hold for any finite value of N . q 2000 Published c by Elsevier Science B.V. All rights reserved.
Physics Letters B, 2000
We explicitly compute the complete three-loop (O(g4)) contribution to the four-point function of ... more We explicitly compute the complete three-loop (O(g4)) contribution to the four-point function of chiral primary current-like operators 〈q̃2q2q̃2q2〉 in any finite N=2 SYM theory. The computation uses N=2 harmonic supergraphs in coordinate space. Dramatic simplifications are achieved by a double insertion of the N=2 SYM linearized action, and application of superconformal covariance arguments to the resulting nilpotent six-point amplitude. The
Nuclear Physics B, 2001
We show that, although the correlator of four stress-tensor multiplets in N = 4 SYM is known to h... more We show that, although the correlator of four stress-tensor multiplets in N = 4 SYM is known to have radiative corrections, certain linear combinations of its components are protected from perturbative renormalisation and remain at their free-field values. This result is valid for weak as well as for strong coupling and for any gauge group. Our argument uses Intriligator's insertion formula, and includes a proof that the possible contact term contributions cannot change the form of the amplitudes. Combining this new non-renormalisation theorem with Maldacena's conjecture allows us to make a prediction for the structure of the corresponding correlator in AdS supergravity. This is verified by first considerably simplifying the strong coupling expression obtained by recent supergravity calculations, and then showing that it does indeed exhibit the expected structure.
Nuclear Physics B, 1999
Four-point functions of gauge-invariant operators in D = 4, N = 4 supersymmetfic Yang-Mills theor... more Four-point functions of gauge-invariant operators in D = 4, N = 4 supersymmetfic Yang-Mills theory are studied using N = 2 harmonic superspace perturbation theory. The results are expressed in terms of differential operators acting on a scalar two-loop integral. The leading singular behaviour is obtained in the limit that two of the points approach one another. We find logarithmic singularities which do not cancel out in the sum of all diagrams. It is confirmed that Green's functions of analytic operators are indeed analytic at this order in perturbation theory.
Nuclear Physics B, 2000
We study the divergence of large-order perturbation theory in the worldline expression for the tw... more We study the divergence of large-order perturbation theory in the worldline expression for the two-loop Euler-Heisenberg QED effective Lagrangian in a constant magnetic field. The leading rate of divergence is identical, up to an overall factor, to that of the one-loop case. From this we deduce, using Borel summation techniques, that the leading behaviour of the imaginary part of the two-loop effective Lagrangian for a constant E field, giving the pair-production rate, is proportional to the one-loop result. This also serves as a test of the mass renormalization, and confirms the earlier analysis by Ritus.
Einstein-Maxwell theory implies the mixing of photons with gravitons in an external electromagnet... more Einstein-Maxwell theory implies the mixing of photons with gravitons in an external electromagnetic eld. This process and its possible observable consequences have been studied at tree level for many years. We use the worldline formalism for obtaining an exact integral representation for the one-loop corrections to this amplitude due to scalars and fermions. We study the structure of this amplitude, and obtain exact expressions for various limiting cases.
Journal of Physics A: Mathematical and Theoretical, 2008
Einstein-Maxwell theory implies the mixing of photons with gravitons in an external electromagnet... more Einstein-Maxwell theory implies the mixing of photons with gravitons in an external electromagnetic field. This process and its possible observable consequences have been studied at tree level for many years. We use the worldline formalism for obtaining an exact integral representation for the one-loop corrections to this amplitude due to scalars and fermions. We study the structure of this amplitude, and obtain exact expressions for various limiting cases. arXiv:0711.0992v2 [hep-th]
Physical Review D, 2006
In a previous paper [G. V. Dunne and C. Schubert, Phys. Rev. D 72, 105004 (2005).PRVDAQ0556-28211... more In a previous paper [G. V. Dunne and C. Schubert, Phys. Rev. D 72, 105004 (2005).PRVDAQ0556-282110.1103/PhysRevD.72.105004], it was shown that the worldline expression for the nonperturbative imaginary part of the QED effective action can be approximated by the contribution of a special closed classical path in Euclidean spacetime, known as a worldline instanton. Here we extend this formalism to compute
Quantum Theory and Symmetries - Proceedings of the 3rd International Symposium, 2004
The Euler-Heisenberg effective action in a self-dual background is remarkably simple at two-loop.... more The Euler-Heisenberg effective action in a self-dual background is remarkably simple at two-loop. This simplicity is due to the inter-relationship between self-duality, helicity and supersymmetry. Applications include two-loop helicity amplitudes, beta-functions and nonperturbative effects. The two-loop Euler-Heisenberg effective Lagrangian for QED in a self-dual background field is naturally expressed in terms of one-loop quantities. This mirrors similar behavior recently found in two-loop amplitudes in N=4 SUSY Yang-Mills theory.
In recent years, the Euler-Heisenberg Lagrangian has been shown to be a useful tool for the analy... more In recent years, the Euler-Heisenberg Lagrangian has been shown to be a useful tool for the analysis of the asymptotic growth of the N-photon amplitudes at large N. Moreover, certain results and conjectures on its imaginary part allow one, using Borel analysis, to make predictions for those amplitudes at large loop orders. Extending work by G.V. Dunne and one of
We present a scalar thick brane configuration arising in a theory of 5D gravity coupled to a self... more We present a scalar thick brane configuration arising in a theory of 5D gravity coupled to a self-interacting scalar field. We start from a classical solution of the field equations and study the physics of linear fluctuations around this background which obey a Schrödinger-like equation. We further focus our attention on a special case in which it is possible to
Journal of High Energy Physics, 2006
We obtain closed-form expressions, in terms of the Faulhaber numbers, for the weak-field expansio... more We obtain closed-form expressions, in terms of the Faulhaber numbers, for the weak-field expansion coefficients of the two-loop Euler-Heisenberg effective Lagrangians in a magnetic or electric field. This follows from the observation that the magnetic worldline Green's function has a natural expansion in terms of the Faulhaber numbers.
Theoretical and Mathematical Physics, 1997
We clarify a discrepancy between two previous calculations of the two-loop QED Euler-Heisenberg L... more We clarify a discrepancy between two previous calculations of the two-loop QED Euler-Heisenberg Lagrangian, both performed in proper-time regularization, by calculating this quantity in dimensional regularization.
Journal of High Energy Physics, 2008
The worldline formalism has in recent years emerged as a powerful tool for the computation of eff... more The worldline formalism has in recent years emerged as a powerful tool for the computation of effective actions and heat kernels. However, implementing nontrivial boundary conditions in this formalism has turned out to be a difficult problem. Recently, such a generalization was developed for the case of a scalar field on the half-space R + × R D−1 , based on an extension of the associated worldline path integral to the full R D using image charges. We present here an improved version of this formalism which allows us to write down non-recursive master formulas for the n -point contribution to the heat kernel trace of a scalar field on the half-space with Dirichlet or Neumann boundary conditions. These master formulas are suitable to computerization. We demonstrate the efficiency of the formalism by a calculation of two new heat-kernel coefficients for the half-space, a 4 and a 9/2 .
Journal of High Energy Physics, 2005
In part 1 of this series compact integral representations had been obtained for the one-loop phot... more In part 1 of this series compact integral representations had been obtained for the one-loop photon-graviton amplitude involving a charged spin 0 or spin 1/2 particle in the loop and an arbitrary constant electromagnetic field. In this sequel, we study the structure and magnitude of the various polarization components of this amplitude on-shell. Explicit expressions are obtained for a number of limiting cases. arXiv:0710.5572v1 [gr-qc]
Journal of High Energy Physics, 2002
We analyze the structure of the imaginary part of the two-loop Euler-Heisenberg QED effective Lag... more We analyze the structure of the imaginary part of the two-loop Euler-Heisenberg QED effective Lagrangian for a constant self-dual background. The novel feature of the two-loop result, compared to one-loop, is that the prefactor of each exponential (instanton) term in the imaginary part has itself an asymptotic expansion. We also perform a high-precision test of Borel summation techniques applied to the weak-field expansion, and find that the Borel dispersion relations reproduce the full prefactor of the leading imaginary contribution.
Journal of High Energy Physics, 2010
We continue an effort to obtain information on the QED perturbation series at high loop orders, a... more We continue an effort to obtain information on the QED perturbation series at high loop orders, and particularly on the issue of large cancellations inside gauge invariant classes of graphs, using the example of the l -loop N -photon amplitudes in the limit of large photons numbers and low photon energies. As was previously shown, high-order information on these amplitudes can be obtained from a nonperturbative formula, due to Affleck et al., for the imaginary part of the QED effective lagrangian in a constant field. The procedure uses Borel analysis and leads, under some plausible assumptions, to a number of nontrivial predictions already at the three-loop level. Their direct verification would require a calculation of this 'Euler-Heisenberg lagrangian' at three-loops, which seems presently out of reach. Motivated by previous work by Dunne and Krasnansky on Euler-Heisenberg lagrangians in various dimensions, in the present work we initiate a new line of attack on this problem by deriving and proving the analogous predictions in the simpler setting of 1+1 dimensional QED. In the first part of this series, we obtain a generalization of the formula of Affleck et al. to this case, and show that, for both Scalar and Spinor QED, it correctly predicts the leading asymptotic behaviour of the weak field expansion coefficients of the two loop Euler-Heisenberg lagrangians.
Physics Letters B, 1998
We consider the one-loop e ective action due to a spinor loop coupled to an abelian vector and ax... more We consider the one-loop e ective action due to a spinor loop coupled to an abelian vector and axial vector eld background. After rewriting this e ective action in terms of an auxiliary non-abelian gauge connection, we use the De Witt expansion to analyze both its anomalous and non-anomalous content. The same transformation allows us to obtain a novel worldline path integral representation for this e ective action which avoids the usual separation into the real and imaginary parts of the Euclidean e ective action, as well as the introduction of auxiliary dimensions. 11.15Bt email: (1) TMLEAFS@APMATHS.UWO.CA/ (2) SCHUBERT@LAPP.IN2P3.FR
Physics Letters B, 1995
We construct the world-line action for a Dirac particle coupled to a classical scalar or pseudo-s... more We construct the world-line action for a Dirac particle coupled to a classical scalar or pseudo-scalar background field. This action can be used to compute loop diagrams and the effective action in the Yukawa model using the world-line path-integral formalism for spinning particles.
Physics Letters B, 1999
The superconformal Ward identities combined with N s 2 harmonic analyticity are used to evaluate ... more The superconformal Ward identities combined with N s 2 harmonic analyticity are used to evaluate two-loop four-point correlation functions of gauge-invariant operators in D s 4, N s 4 supersymmetric Yang-Mills theory in terms of the well-known one-loop box integral. The result is confirmed by a direct numerical computation. q 1999 Elsevier Science B.V. All rights reserved.
Physics Letters B, 2000
Ž It is shown that certain extremal correlators in four-dimensional N s 2 superconformal field th... more Ž It is shown that certain extremal correlators in four-dimensional N s 2 superconformal field theories including N s 4 . super-Yang-Mills as a special case have a free-field functional form. It is further argued that the coupling constant dependence receives no correction beyond the lowest order. These results hold for any finite value of N . q 2000 Published c by Elsevier Science B.V. All rights reserved.
Physics Letters B, 2000
We explicitly compute the complete three-loop (O(g4)) contribution to the four-point function of ... more We explicitly compute the complete three-loop (O(g4)) contribution to the four-point function of chiral primary current-like operators 〈q̃2q2q̃2q2〉 in any finite N=2 SYM theory. The computation uses N=2 harmonic supergraphs in coordinate space. Dramatic simplifications are achieved by a double insertion of the N=2 SYM linearized action, and application of superconformal covariance arguments to the resulting nilpotent six-point amplitude. The
Nuclear Physics B, 2001
We show that, although the correlator of four stress-tensor multiplets in N = 4 SYM is known to h... more We show that, although the correlator of four stress-tensor multiplets in N = 4 SYM is known to have radiative corrections, certain linear combinations of its components are protected from perturbative renormalisation and remain at their free-field values. This result is valid for weak as well as for strong coupling and for any gauge group. Our argument uses Intriligator's insertion formula, and includes a proof that the possible contact term contributions cannot change the form of the amplitudes. Combining this new non-renormalisation theorem with Maldacena's conjecture allows us to make a prediction for the structure of the corresponding correlator in AdS supergravity. This is verified by first considerably simplifying the strong coupling expression obtained by recent supergravity calculations, and then showing that it does indeed exhibit the expected structure.
Nuclear Physics B, 1999
Four-point functions of gauge-invariant operators in D = 4, N = 4 supersymmetfic Yang-Mills theor... more Four-point functions of gauge-invariant operators in D = 4, N = 4 supersymmetfic Yang-Mills theory are studied using N = 2 harmonic superspace perturbation theory. The results are expressed in terms of differential operators acting on a scalar two-loop integral. The leading singular behaviour is obtained in the limit that two of the points approach one another. We find logarithmic singularities which do not cancel out in the sum of all diagrams. It is confirmed that Green's functions of analytic operators are indeed analytic at this order in perturbation theory.
Nuclear Physics B, 2000
We study the divergence of large-order perturbation theory in the worldline expression for the tw... more We study the divergence of large-order perturbation theory in the worldline expression for the two-loop Euler-Heisenberg QED effective Lagrangian in a constant magnetic field. The leading rate of divergence is identical, up to an overall factor, to that of the one-loop case. From this we deduce, using Borel summation techniques, that the leading behaviour of the imaginary part of the two-loop effective Lagrangian for a constant E field, giving the pair-production rate, is proportional to the one-loop result. This also serves as a test of the mass renormalization, and confirms the earlier analysis by Ritus.
Einstein-Maxwell theory implies the mixing of photons with gravitons in an external electromagnet... more Einstein-Maxwell theory implies the mixing of photons with gravitons in an external electromagnetic eld. This process and its possible observable consequences have been studied at tree level for many years. We use the worldline formalism for obtaining an exact integral representation for the one-loop corrections to this amplitude due to scalars and fermions. We study the structure of this amplitude, and obtain exact expressions for various limiting cases.
Journal of Physics A: Mathematical and Theoretical, 2008
Einstein-Maxwell theory implies the mixing of photons with gravitons in an external electromagnet... more Einstein-Maxwell theory implies the mixing of photons with gravitons in an external electromagnetic field. This process and its possible observable consequences have been studied at tree level for many years. We use the worldline formalism for obtaining an exact integral representation for the one-loop corrections to this amplitude due to scalars and fermions. We study the structure of this amplitude, and obtain exact expressions for various limiting cases. arXiv:0711.0992v2 [hep-th]