Large rank Wilson loops in N=2 superconformal QCD at strong coupling

TL;DR

This paper analyzes large-rank Wilson loops in N=2 superconformal QCD at strong coupling, revealing distinct behaviors for symmetric and antisymmetric representations and uncovering non-analytic phenomena linked to eigenvalue splitting.

Contribution

It introduces a novel calculation method connecting Wilson loops to Fermi and Bose gas models, revealing non-analyticities and potential links to Kondo physics.

Findings

Antisymmetric loops are coupling-independent at strong coupling.

Symmetric loops grow exponentially with the coupling.

Non-analyticity in symmetric loops resembles Bose-Einstein condensation.

Abstract

We compute the expectation values of circular Wilson loops in large representations at strong coupling, in the large-N limit of the N=2 superconformal theory with SU(N) gauge group and 2N hypermultiplets. Employing Pestun's matrix integral, we focus attention on symmetric and antisymmetric representations with ranks of order N. We find that large rank antisymmetric loops are independent of the coupling at strong 't Hooft coupling while symmetric Wilson loops grow exponentially with it. Symmetric loops display a non-analyticity as a function of the rank, characterized by the splitting of a single matrix model eigenvalue from the continuum, bearing close resemblance to Bose-Einstein condensation in an ideal gas. We discuss implications of these for a putative large-N string dual. The method of calculation we adopt makes explicit the connection to Fermi and Bose gas descriptions and also suggests a tantalizing connection of the above system to a multichannel Kondo model.