Cusped Wilson lines in symmetric representations

TL;DR

This paper investigates cusped Wilson lines in symmetric representations of N=4 super Yang-Mills, providing holographic descriptions, testing conjectured relations, and proposing exponentiation behavior for large k.

Contribution

It offers a holographic D3-brane description for cusped Wilson loops in symmetric representations and proposes a general exponentiation conjecture for large k.

Findings

Holographic D3-brane description matches small cusp angle and large k limits.

Confirmed relation between Bremsstrahlung function and circular loop expectation value.

Proposed all-order exponentiation for large k symmetric Wilson loops.

Abstract

We study the cusped Wilson line operators and Bremsstrahlung functions associated to particles transforming in the rank-$k$ symmetric representation of the gauge group $U(N)$ for ${\cal N} = 4$ super Yang-Mills. We find the holographic D3-brane description for Wilson loops with internal cusps in two different limits: small cusp angle and $k\sqrt{\lambda}\gg N$. This allows for a non-trivial check of a conjectured relation between the Bremsstrahlung function and the expectation value of the 1/2 BPS circular loop in the case of a representation other than the fundamental. Moreover, we observe that in the limit of $k\gg N$, the cusped Wilson line expectation value is simply given by the exponential of the 1-loop diagram. Using group theory arguments, this eikonal exponentiation is conjectured to take place for all Wilson loop operators in symmetric representations with large $k$, independently of the contour on which they are supported.