Wilson Loops in 5d $${\mathcal{N} = 1}$$ SCFTs and AdS/CFT

Abstract

We consider \({\frac{1}{2}}\)-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.