arXiv subjects

C. Schubert

Publications and source records attributed to C. Schubert.

At least 37 records · Page 2Linked to original sources

arXiv2013

An algebraic/numerical formalism for one-loop multi-leg amplitudes

We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which naturally isolates infrared divergences by construction. We prove that for N>4, higher dimensional integrals can be avoided. We derive many useful relations which allow for algebraic simplifications of one-loop amplitudes. We introduce a form factor representation of tensor integrals which contains no inverse Gram determinants by choosing a convenient set of basis integrals. For the evaluation of these basis integrals we propose two methods: An evaluation based on the analytical representation, which is fast and accurate away from exceptional kinematical configurations, and a robust numerical one, based on multi-dimensional contour deformation. The formalism can be implemented straightforwardly into a computer program to calculate next-to-leading order corrections to multi-particle processes in a largely automated way.

hep-ph↗

arXiv2013

Infrared divergences, mass shell singularities and gauge dependence of the dynamical fermion mass

We study the behavior of the dynamical fermion mass when infrared divergences and mass shell singularities are present in a gauge theory. In particular, in the massive Schwinger model in covariant gauges we find that the pole of the fermion propagator is divergent and gauge dependent at one loop, but the leading singularities cancel in the quenched rainbow approximation. On the other hand, in physical gauges, we find that the dynamical fermion mass is finite and gauge independent at least up to one loop.

hep-th↗

arXiv2013

QED effective action for an O(2)xO(3) symmetric field in the full mass range

An interesting class of background field configurations in QED are the O(2)xO(3) symmetric fields. Those backgrounds have some instanton-like properties and yield a one-loop effective action that is highly nontrivial but amenable to numerical calculation, for both scalar and spinor QED. Here we use the recently developed "partial-wave-cutoff method" for a numerical analysis of both effective actions in the full mass range. In particular, at large mass we are able to match the asymptotic behavior of the physically renormalized effective action against the leading two mass levels of the inverse mass (or heat kernel) expansion. At small mass we obtain good numerical results even in the massless case for the appropriately (unphysically) renormalized effective action after the removal of the chiral anomaly term through a small radial cutoff factor. In particular, we show that the effective action after this removal remains finite in the massless limit, which also provides indirect support for M. Fry's hypothesis that the QED effective action in this limit is dominated by the chiral anomaly term.

hep-th↗

arXiv2012

On the low energy limit of one loop photon-graviton amplitudes

We present first results of a systematic study of the structure of the low energy limit of the one-loop photon-graviton amplitudes induced by massive scalars and spinors. Our main objective is the search of KLT-type relations where effectively two photons merge into a graviton. We find such a relation at the graviton-photon-photon level. We also derive the diffeomorphism Ward identity for the 1PI one graviton - N photon amplitudes.

hep-th↗

arXiv2012

A Compact Representation of the Three-Gluon Vertex

The three-gluon vertex is a basic object of interest in nonabelian gauge theory. It contains important structural information, in particular on infrared divergences, and also figures prominently in the Schwinger-Dyson equations. At the one-loop level, it has been calculated and analyzed by a number of authors. Here we use the worldline formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation. The SUSY - related sum rule found by Binger and Brodsky follows from an off-shell extension of the Bern-Kosower replacement rules. We explain the relation of the structure of our representation to the low-energy effective action.

hep-ph↗

arXiv2012

Photon-Graviton Amplitudes from the Effective Action

We report on the status of an ongoing effort to calculate the complete one-loop low-energy effective actions in Einstein-Maxwell theory with a massive scalar or spinor loop, and to use them for obtaining the explicit form of the corresponding M-graviton/N-photon amplitudes. We present explicit results for the effective actions at the one-graviton four-photon level, and for the amplitudes at the one-graviton two-photon level. As expected on general grounds, these amplitudes relate in a simple way to the corresponding four-photon amplitudes. We also derive the gravitational Ward identity for the 1PI one-graviton -- N photon amplitude.

hep-th↗

arXiv2010

Euler-Heisenberg lagrangians and asymptotic analysis in 1+1 QED, part 1: Two-loop

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.

hep-th↗

arXiv2009

Worldline Approach to QFT on Manifolds with Boundary

We use the image charge method to compute the trace of the heat kernel for a scalar field on a flat manifold with boundary, representing the trace by means of a worldline path integral and obtain useful non-iterative master formulae for n insertions of the scalar potential. We discuss possible extensions of the method.

hep-th↗

arXiv2009

Three-loop Euler-Heisenberg Lagrangian and asymptotic analysis in 1+1 QED

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 the authors to the three-loop level, but in the simpler context of 1+1 dimensional QED, we calculate the corresponding Euler-Heisenberg Lagrangian, analyse its weak field expansion, and study the congruence with predictions obtained from worldline instantons. We discuss the relevance of these issues for Cvitanovic's conjecture.

hep-th↗

arXiv2008

Mass gap for gravity localized on Weyl thick branes

We study the properties of a previously found family of thick brane configurations in a pure geometric Weyl integrable 5D space time, a non-Riemannian generalization of Kaluza-Klein (KK) theory involving a geometric scalar field. Thus the 5D theory describes gravity coupled to a self-interacting scalar field which gives rise to the structure of the thick branes. Analyzing the graviton spectrum for this class of models, we find that a particularly interesting situation arises for a special case in which the 4D graviton is separated from the KK gravitons by a mass gap. The corresponding effective Schroedinger equation has a modified Poeschl-Teller potential and can be solved exactly. Apart from the massless 4D graviton, it contains one massive KK bound state, and the continuum spectrum of delocalized KK modes. We discuss the mass hierarchy problem, and explicitly compute the corrections to Newton's law in the thin brane limit.

hep-th↗

arXiv2008

Photon-graviton mixing in an electromagnetic field

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.

hep-th↗

arXiv2007

One loop photon-graviton mixing in an electromagnetic field: Part 2

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.

gr-qc↗

arXiv2006

Closed-form weak-field expansion of two-loop Euler-Heisenberg Lagrangians

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.

hep-th↗

arXiv2004

Supersymmetry on AdS3 and AdS4

We consider a supersymmetric extension of the algebra associated with three and four dimensional Anti de Sitter space. A representation of the supersymmetry operators in superspace is given. Supersymmetry invariant models are constructed for the superspace associated with AdS3.

hep-th↗

arXiv2001

Calculation of 1-loop Hexagon Amplitudes in the Yukawa Model

We calculate a class of one-loop six-point amplitudes in the Yukawa model. The construction of multi-particle amplitudes is done in the string inspired formalism and compared to the Feynman diagrammatic approach. We show that there exists a surprisingly efficient way of calculating such amplitudes by using cyclic identities of kinematic coefficients and discuss in detail cancellation mechanisms of spurious terms. A collection of formulas which are useful for the calculation of massless hexagon amplitudes is given.

hep-ph↗

arXiv2000

Four - Point Functions of Chiral Primary Operators in N=4 SYM

We discuss recent progress in the determination of correlators of chiral primary operators in N=4 Super-Yang-Mills theory, based on a combination of superconformal covariance arguments in N=2 harmonic superspace, and Intriligator's insertion formula. Applying this technique to the calculation of the supercurrent four - point function we obtain a compact and explicit result for its three-loop contribution with comparatively little effort.

hep-th↗

arXiv2000

Three-Loop Four-Point Correlator in N=4 SYM

We explicitly compute the complete three-loop (O(g^4)) contribution to the four-point function of chiral primary current-like operators <(q)^2 q^2 (q)^2 q^2> 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 result involves polylogarithms up to fourth order of the conformal cross ratios. It becomes particularly simple in the N=4 special case.

hep-th↗

arXiv1999

Extremal correlators in four-dimensional SCFT

It is shown that certain extremal correlators in four-dimensional N=2 superconformal field theories (including N=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_c.

hep-th↗