Wilson Loops in 5d N=1 SCFTs and AdS/CFT

TL;DR

This paper computes and compares the large N limit of 1/2-BPS Wilson loops in 5d superconformal field theories using localization and supergravity duals, revealing agreement and detailed structure for various representations.

Contribution

It provides the first detailed comparison of Wilson loop expectation values in 5d SCFTs from both field theory and holography, including multiple representations and quiver theories.

Findings

Agreement between localization and supergravity in large N limit

Factorization of Wilson loops in anti-symmetric representations

Complex behavior in symmetric representations

Abstract

We consider 1/2-BPS circular Wilson loops in a class of 5d superconformal field theories on S^5. The large N limit of the vacuum expectation values of Wilson loops are computed both by localization in the field theory and by evaluating the fundamental string and D4-brane actions in the dual massive IIA supergravity background. We find agreement in the leading large N limit for a rather general class of representations, including fundamental, anti-symmetric and symmetric representations. For single node theories the match is straightforward, while for quiver theories, the Wilson loop can be in different representations for each node. We highlight the two special cases when the Wilson loop is in either in all symmetric or all anti-symmetric representations. In the anti-symmetric case, we find that the vacuum expectation value factorizes into distinct contributions from each quiver node. In the dual supergravity description, this corresponds to probe D4-branes wrapping internal S^3 cycles. The story is more complicated in the symmetric case and the vacuum expectation value does not exhibit factorization.