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

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_ξgauge. The conformal transformation law of the gauge field turns out to be ξ-independent. We construct the scalar field redefinition which relates the 't Hooft and R_ξgauge 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.

14 pages, latex, no figures; references and comments added, the final version to appear in PLB

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Cited by in corpus (7)

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• Relaxed super self-duality and N = 4 SYM at two loops
• Hypermultiplet dependence of one-loop effective action in the $\mathcal{N}=2$ superconformal theories
• Low energy dynamics from deformed conformal symmetry in quantum 4D N = 2 SCFTs
• BRST-BV quantization of gauge theories with global symmetries