Wilson loops in 5d long quiver gauge theories

TL;DR

This paper computes Wilson loop expectation values in 5d long quiver gauge theories with holographic duals, revealing a match between field theory and supergravity results and providing new insights into their geometric duals.

Contribution

It introduces a method to calculate Wilson loops in 5d quiver gauge theories using localization and identifies their holographic D3-brane duals, including the geometric interpretation.

Findings

Wilson loop expectation values expressed via Bloch-Wigner functions

Exact holographic duals identified as D3-branes in supergravity

Enhanced scaling behavior observed for fundamental Wilson loops

Abstract

Quiver gauge theories with a large number of nodes host a wealth of Wilson loop operators. Expectation values are obtained, using supersymmetric localization, for Wilson loops in the antisymmetric representations associated with each individual gauge node, for a sample of 5d long quiver gauge theories whose UV fixed points have holographic duals in Type IIB. The sample includes the $T_N$ theories and the results are uniformly given in terms of Bloch-Wigner functions. The holographic representation of the Wilson loops is identified. It comprises, for each supergravity solution, a two-parameter family of D3-branes which exactly reproduce the field theory results and identify points in the internal space with the faces of the associated 5-brane web. The expectation values of (anti)fundamental Wilson loops exhibit an enhanced scaling for many operators, which matches between field theory and supergravity.