A covariant representation of the Ball-Chiu vertex

Abstract

In nonabelian gauge theory the three-gluon vertex function contains important structural information, in particular on infrared divergences, and is also an essential ingredient in the Schwinger-Dyson equations. Much effort has gone into analyzing its general structure, and at the one-loop level also a number of explicit computations have been done, using various approaches. Here we use the string-inspired formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation in all cases. The vertex is computed fully off-shell and in dimensionally continued form, so that it can be used as a building block for higher-loop calculations. We find that the Bern-Kosower loop replacement rules, originally derived for the on-shell case, hold off-shell as well. We explain the relation of the structure of this representation to the low-energy effective action, and establish the precise connection with the standard Ball-Chiu decomposition of the vertex. This allows us also to predict that the vanishing of the completely antisymmetric coefficient function S of this decomposition is not a one-loop accident, but persists at higher loop orders. The sum rule found by Binger and Brodsky, which leads to the vanishing of the one-loop vertex in N=4 SYM theory, in the present approach relates to worldline supersymmetry.

32 pages, 1 figure, final revised version (calculation of the two-point functions included, minor corrections, references added)

References in corpus (3)

• Pinch Technique: Theory and Applications
• The Form Factors of the Gauge-Invariant Three-Gluon Vertex
• String-inspired representations of photon/gluon amplitudes

Cited by in corpus (25)

• Effects of divergent ghost loops on the Green's functions of QCD
• Particles with non abelian charges
• Multiphoton amplitudes and generalized LKF transformation in Scalar QED
• Dressed scalar propagator in a non-abelian background from the worldline formalism
• Worldline master formulas for the dressed electron propagator, part 1: Off-shell amplitudes
• Off-shell two loop QCD vertices
• Symmetric point quartic gluon vertex and momentum subtraction
• String-inspired representations of photon/gluon amplitudes
• Color-kinematics duality from the Bern-Kosower formalism
• QCD gluon vertices from the string-inspired formalism
• QCD effective charge from the three-gluon vertex of the background-field method
• On the self-consistency of off-shell Slavnov-Taylor identities in QCD
• Compton-like scattering of a scalar particle with N photons and one graviton
• Exploring dynamical gluon mass generation in three dimensions
• Integral representations combining ladders and crossed-ladders
• Three-point vertex functions in Yang-Mills Theory and QCD in Landau gauge
• The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators
• Off-shell Ward identities for N-gluon amplitudes
• Multiphoton amplitudes and generalized LKF transformation in scalar QED using the worldline formalism
• $U(N)$ Yang-Mills in non-commutative space time
• Spinning Particles in Quantum Mechanics and Quantum Field Theory
• One-loop $N$-point correlators in pure gravity
• Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies
• Non-perturbative gauge transformations of arbitrary fermion correlation functions in quantum electrodynamics
• Three easy exercises in off-shell string-inspired methods