Effective action of beta-deformed N=4 SYM theory and AdS/CFT

TL;DR

This paper calculates the one-loop effective action in a beta-deformed N=4 SYM theory, showing that at large N and real deformation parameter, the effective action simplifies and aligns with supergravity predictions, indicating a non-renormalization property.

Contribution

It provides the first detailed one-loop analysis of the effective action in beta-deformed N=4 SYM, revealing large N simplifications and consistency with AdS/CFT duality predictions.

Findings

Effective action depends on beta at finite N but not at large N for real beta.

Large N limit matches supergravity D3-brane probe results.

Suggests a non-renormalization theorem for the 4-derivative term in the real beta case.

Abstract

We compute the one-loop effective action in \N=1 conformal SU(N) gauge theory which is an exactly marginal deformation of the \N=4 SYM theory. We consider an abelian background of constant \N = 1 gauge field and single chiral scalar. While for finite N the effective action depends non-trivially on the deformation parameter \beta, this dependence disappears in the large N limit if the parameter \beta is real. This conclusion matches the strong-coupling prediction coming from the form of a D3-brane probe action in the dual supergravity background: for the simplest choice of the D3-brane position the probe action happens to be the same as for a D3-brane in AdS_5 x S^5 placed parallel to the boundary of AdS_5. This suggests that in the real \beta deformation case there exists a large N non-renormalization theorem for the 4-derivative term in the action.