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

TL;DR

The paper computes the leading large-N behavior of 1/2-BPS circular Wilson loops in a class of 5d N=1 SCFTs and their AdS/CFT duals in massive IIA string theory. Using localization and matrix-model techniques on the field theory side, and D4-brane/F1-string probes on the gravity side, it derives explicit exponentiated forms for Wilson loops in fundamental, antisymmetric, and symmetric representations, including quiver generalizations. A key finding is the factorization of antisymmetric contributions across quiver nodes, in contrast to symmetric representations which generally do not factorize, with gravity offering a brane-based interpretation. The results are corroborated by matching gravity actions and a holographic free-energy computation, providing a concrete quantitative test of AdS/CFT in a non-renormalizable yet UV-complete 5d setting and suggesting directions for refining holographic duals to capture flavor data and brane backreaction.

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.

Figures (7)

• Figure 1: Insertion of a Wilson line in anti-symmetric representation shifts part of the eigenvalues by a constant, or equivalently an excitation of a "hole" in the eigenvalues.
• Figure 2: Insertion of a Wilson line in symmetric representation corresponds to exciting one of the eigenvalues to a large value, or equivalently an excitation of a "particle" in the Fermi sea.
• Figure 3: Wilson lines in general representations can be described either as the excitation of several non-interacting particles above the Fermi sea (left) or the excitation of non-interacting holes (right). The two descriptions correspond to a Young diagram and its dual, i.e. taking the transpose could be thought as a Bogoliubov-like transformation.
• Figure 4: Wilson lines in symmetric representations for the quiver theories ($n>1$) can be described by excitations of interacting particles above the Fermi sea. The size of the Fermi sea scales as $\sqrt{n}$. There are several different types of particle species, corresponding to different nodes of the quiver. In this figure the different particle species are represented by different types of dots.
• Figure 5: Vanishing 2-cycles $\Sigma_i$ at the pole of the semi-$S^4$ and dual 2-cycles $\tilde{\Sigma}_i$ ($1\le i \le n-1$) spanned by coordinates $\alpha$ and $\theta_1$ ($S^1$ transverse to the picture).