Quantum metamorphosis of conformal symmetry in N = 4 super Yang-Mills theory

TL;DR

This paper investigates how conformal symmetry in N=4 super Yang-Mills theory is altered by quantum effects, revealing a 'metamorphosis' that aligns with AdS/CFT correspondence insights.

Contribution

It derives the conformal Ward identity and computes quantum modifications of conformal transformations in N=4 SYM, connecting these to D3-brane dynamics in AdS5 x S5.

Findings

Quantum conformal transformations match D3-brane behavior.

Scalar field modifications agree with previous studies.

Results shed light on the quantum structure of conformal symmetry in gauge theories.

Abstract

In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occurs for conformal symmetry in quantum Yang-Mills theories with vanishing beta function, such as the N = 4 super Yang-Mills theory. More recently, Jevicki et al demonstrated that the quantum metamorphosis of conformal symmetry sheds light on the nature of the AdS/CFT correspondence. In this paper, we derive the conformal Ward identity for the bosonic sector of the N = 4 super Yang-Mills theory using the background field method. We then compute the leading quantum modification of the conformal transformation for a specific Abelian background which is of interest in the context of the AdS/CFT correspondence. In the case of scalar fields, our final result agrees with that of Jevicki et al. The resulting vector and scalar transformations coincide with those which are characteristic of a D3-brane embedded in AdS5 x S5.