Antisymmetric Wilson loops in N $$ \mathcal{N} $$ = 4 SYM beyond the planar limit

Abstract

We study the 1 2 -BPS circular Wilson loop in the totally antisymmetric representation of the gauge group in N = 4 supersymmetric Yang-Mills. This observable is captured by a Gaussian matrix model with appropriate insertion. We compute the first 1/N correction at leading order in 't Hooft coupling by means of the matrix model loop equations. Disagreement with the 1-loop effective action of the holographically dual D5-brane suggests the need to account for gravitational backreaction on the string theory side.

Phase transition of anti-symmetric Wilson loops in N = 4 $$ \mathcal{N}=4 $$ SYM

“…In section 2, we compute the small λ expansion of the generating function (1.5) and show that our result of J 1 (z) reproduces the result in [18]. In section 3, we compute the higher order corrections J n (z) in the 1/N expansion (1.5) using the topological recursion of the Gaussian matrix model.…”

“…Here, the extra factor e λk 2 8N 2 comes from the U(1) part of U(N ) gauge theory [18] and W A k in (1.2) denotes the expectation value of the Wilson loop in SU(N ) gauge theory. This generating function has a simple expression in the Gaussian matrix model…”

“…The first approach is to regard the operator det(1 + ze M ) as a part of the potential of matrix integral 6) and study the large N behavior of eigenvalue distribution under this modified potential. This approach was recently considered in [18]. The second one is to treat the insertion det(1 + ze M ) as an operator in the original Gaussian matrix model.…”

“…However, when λ ∼ N 2 we should take into account the backreaction of the operator det(1 + ze M ). As suggested in [18], in this regime we can take a scaling limit N, λ → ∞ with ξ = √ λ N : fixed.…”

“…However, a mismatch at the subleading order in the 1/N expansion was reported for both symmetric and antisymmetric representations [12][13][14][15] (see also [16] for a review of the status of this problem). Recently, the first 1/N correction of Wilson loops was computed for both symmetric [17] and anti-symmetric [18] representations, but the mismatch still remains as an issue.…”