On Exactly Marginal Deformations of N=4 SYM and Type IIB Supergravity on AdS_5 * S^5

TL;DR

This paper explores the construction of supergravity solutions dual to exactly marginal deformations of N=4 SYM, revealing insights into their conformal properties and beta functions through perturbative analysis.

Contribution

It explicitly constructs the supergravity duals of exactly marginal deformations of N=4 SYM up to second order and analyzes their beta functions at third order.

Findings

Deformed solutions are explicitly constructed at second order.

Marginal but not exactly marginal deformations lead to non-conformal solutions.

Beta functions match between field theory and supergravity at third order.

Abstract

N=4 supersymmetric Yang-Mills theory with gauge group SU(n) (n>=3) is believed to have two exactly marginal deformations which break the supersymmetry to N=1. We discuss the construction of the string theory dual to these deformations, in the supergravity approximation, in a perturbation series around the AdS_5 * S^5 solution. We construct explicitly the deformed solution at second order in the deformation. We show that deformations which are marginal but not exactly marginal lead to a non-conformal solution with a logarithmically running coupling constant. Surprisingly, at third order in the deformation we find the same beta functions for the couplings in field theory and in supergravity, suggesting that the leading order beta functions (or anomalous dimensions) do not depend on the gauge coupling (the coefficient is not renormalized).