An Exact Prediction of N=4 SUSYM Theory for String Theory

TL;DR

This paper provides an exact calculation of Wilson loop expectation values in N=4 SUSY Yang-Mills theory, linking gauge theory results with string theory predictions via AdS/CFT duality, and confirms their agreement at various orders.

Contribution

It introduces an exact method for computing Wilson loop expectation values in N=4 SUSY YM and compares these with string theory predictions, confirming their consistency.

Findings

Gauge theory results match string theory at large g^2 N

Exact calculation of Wilson loops to all orders in coupling

Established a relation between Wilson loops and inversion symmetry

Abstract

We propose that the expectation value of a circular BPS-Wilson loop in N=4 SUSYM can be calculated exactly, to all orders in a 1/N expansion and to all orders in g^2 N. Using the AdS/CFT duality, this result yields a prediction of the value of the string amplitude with a circular boundary to all orders in alpha' and to all orders in g_s. We then compare this result with string theory. We find that the gauge theory calculation, for large g^2 N and to all orders in the 1/N^2 expansion does agree with the leading string theory calculation, to all orders in g_s and to lowest order in alpha'. We also find a relation between the expectation value of any closed smooth Wilson loop and the loop related to it by an inversion that takes a point along the loop to infinity, and compare this result, again successfully, with string theory.