Dual expansions of N=4 super Yang-Mills theory via IIB superstring theory

TL;DR

This paper explores the duality between IIB superstring theory and N=4 super Yang-Mills theory at finite coupling, analyzing a strong-coupling expansion and its implications for correlation functions and string quantization.

Contribution

It introduces a novel strong-coupling expansion as the S-dual of the planar expansion and investigates its effects on correlation functions and string quantization.

Findings

The strong-coupling expansion is the S-dual of the planar expansion.

Correlation functions are expressed as sums of triangle integrals without poles.

Relations between string quantization and N=4 topological string are established.

Abstract

We examine the dual correspondence between holographic IIB superstring theory and N=4 super Yang-Mills theory at finite values of the coupling constants. In particular we analyze a field theory strong-coupling expansion which is the S-dual of the planar expansion. This expansion arises naturally as the AdS/CFT dual of the IIB superstring scattering amplitudes given a genus truncation property due to modular invariance. The space-time structure of the contributions to the field theory four-point correlation functions obtained from the IIB scattering elements is investigated in the example of the product of four conserved stress tensors, and is expressed as an infinite sum of field theory triangle integrals. The OPE structure of these contributions to the stress tensor four-point function is analyzed and shown not to give rise to any poles. Quantization of the string in the background of a five-form field strength is performed through a covariantized background field approach, and relations to the N=4 topological string are found.