On quantum deformation of conformal symmetry: Gauge dependence via field redefinitions

TL;DR

This paper investigates how quantum deformation of conformal symmetry in N=4 super Yang-Mills theory depends on gauge choices, demonstrating gauge dependence and constructing explicit field redefinitions between different gauges.

Contribution

It explicitly computes the gauge-dependent quantum deformation of conformal symmetry and constructs field redefinitions relating different gauge results, highlighting intrinsic deformation properties.

Findings

Quantum deformation depends on gauge choice.

Explicit field redefinition relates 't Hooft and R_xi gauges.

Conformal transformations form a realization in 't Hooft gauge.

Abstract

The effective action in gauge theories is known to depend on a choice of gauge fixing conditions. This dependence is such that any change of gauge conditions is equivalent to a field redefinition in the effective action. In this sense, the quantum deformation of conformal symmetry in the N = 4 super Yang-Mills theory, which was computed in 't Hooft gauge in hep-th/9808039 and hep-th/0203236, is gauge dependent. The deformation is an intrinsic property of the theory in that it cannot be eliminated by a local choice of gauge (although we sketch a field redefinition induced by a nonlocal gauge which, on the Coulomb branch of the theory, converts the one-loop quantum-corrected conformal transformations to the classical ones). We explicitly compute the deformed conformal symmetry in R_\xi gauge. The conformal transformation law of the gauge field turns out to be \xi-independent. We construct the scalar field redefinition which relates the 't Hooft and R_\xi gauge results. A unique feature of 't Hooft gauge is that it makes it possible to consistently truncate the one-loop conformal deformation to the terms of first order in derivatives of the fields such that the corresponding transformations form a field realization of the conformal algebra.