Self-Dual Effective Action of N=4 Super-Yang Mills

TL;DR

This paper investigates the self-duality of the low energy effective action of N=4 Super-Yang Mills, deriving conditions for self-duality, and compares it with D3-brane descriptions in AdS_5 x S_5, finding agreement up to six derivatives.

Contribution

It derives the conditions for self-duality of the effective action starting from leading terms and compares the results with D3-brane probe descriptions, revealing consistency up to six derivatives.

Findings

Conditions for self-duality are established.

Effective action matches D3-brane description up to six derivatives.

Reinterpretation of scalar separation involves gauge field strength redefinition.

Abstract

The full low energy effective action of N=4 SYM is believed to be self-dual. Starting with the first two leading terms in a momentum expansion of this effective action, we perform a duality transformation and find the conditions for self-duality. These determine some of the higher order terms. We compare the effective action of N=4 SYM with the probe-source description of type II_B D3-branes in the AdS_5 \times S_5 background. We find agreement up to six derivative terms if we identify the separation of the 3-branes with a redefinition of the gauge scalar that involves the gauge field strength.