Wilson loops in Large Symmetric Representations through a Double-Scaling Limit

TL;DR

This paper derives exact formulas for large symmetric Wilson loops in certain supersymmetric gauge theories, exploring their behavior in a double-scaling limit and comparing with holographic results.

Contribution

It provides new exact formulas for Wilson loops in large symmetric representations in the double-scaling limit, including analytic results for specific cases and asymptotic series expansions.

Findings

Exact formulas for Wilson loops in the double-scaling limit.

Analytic solutions for SU(2) and U(2) cases.

Comparison with holographic predictions in the large N, k regime.

Abstract

We derive exact formulas for circular Wilson loops in the $\mathcal{N}=4$ and $\mathcal{N}=2^{* }$ theories with gauge groups $U(N)$ and $SU(N)$ in the $k$-fold symmetrized product representation. The formulas apply in the limit of large $k$ and small Yang-Mills coupling $g$, with fixed effective coupling $\kappa\equiv g^2k$, and for any finite $N$. In the $SU(2)$ and $U(2)$ cases, closed analytic formulas are obtained for any $k$, while the $1/k$ series expansions are asymptotic. In the $N\gg 1$ limit, with $N\ll k$, there is an overlapping regime where the formulas can be confronted with results from holography. Simple formulas for correlation functions between the $k$-symmetric Wilson loops and chiral primary operators are also given.