Exact results for static and radiative fields of a quark in N=4 super Yang-Mills

TL;DR

This paper derives an exact formula for the expectation value of certain operators in N=4 super Yang-Mills theory with a static quark, unifying previous results and providing insights into energy loss due to radiation.

Contribution

It presents an exact expression for operator expectation values in N=4 SYM with a static quark, extending beyond the D-brane probe approximation.

Findings

Agreement with previous computations of different observables.

Proposed an exact formula for operator expectation values.

Provided an expression for energy loss by radiation.

Abstract

In this work (which supersedes our previous preprint arXiv:1112.2345) we determine the expectation value of the N=4$ SU(N) SYM Lagrangian density operator in the presence of an infinitely heavy static particle in the symmetric representation of SU(N), by means of a D3-brane probe computation. The result that we obtain coincides with two previous computations of different observables, up to kinematical factors. We argue that these agreements go beyond the D-brane probe approximation, which leads us to propose an exact formula for the expectation value of various operators. In particular, we provide an expression for the total energy loss by radiation of a heavy particle in the fundamental representation.