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

TL;DR

The paper addresses how to obtain exact, nonperturbative information about static and radiative fields produced by a heavy quark in ${ m SU}(N)$ ${\cal N}=4$ SYM by exploiting AdS/CFT duality and exact Wilson-loop correlators. It derives an explicit one-point function for the Lagrangian density ${\cal O}_{F^2}$ in the presence of a static heavy probe in the $k$-symmetric representation via a D3-brane, and shows that this coefficient matches results from independent D3-brane calculations and Wilson-loop/OPE analyses, hinting at an exact formula valid beyond the probe limit. For the fundamental representation, the authors propose an exact expression for ${\langle {\cal O}_{F^2}(\vec x)\rangle}$ in terms of generalized Laguerre polynomials ${L_n^{\alpha}}$, consistent with known large-$\lambda$/large-$N$ limits and with the symmetric-representation radiative power formula $P_{S_k}$. They further connect these results to exact two-point functions of Wilson loops with chiral primary operators, and to the radiated power for arbitrary timelike trajectories, suggesting a unified, representation-wide exact structure in ${\cal N}=4$ SYM.

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.