Abstract
We study 1/2 BPS Wilson loops in 3d $\mathcal{N}=4$ $U(N)$ Yang-Mills theory with one adjoint and $N_f$ fundamental hypermultiplets from the Fermi gas approach. By numerical fitting, we find the first few worldsheet instanton corrections to the Wilson loops with winding numbers 1, 2 and 3. We verify that our Fermi gas results are consistent with the matrix model results in the planar limit.
Highlights
Correctly reproduces the N 3/2 scaling of free energy expected from the holographically dual M-theory on AdS4 × S7/Zk [4]
We will study the vacuum expectation value (VEV) of 1/2 BPS Wilson loops in the Nf matrix model
We have studied the Wilson loops in the Nf matrix model from the Fermi gas approach
Summary
The gauge kinetic term is irrelevant in IR and the S3 partition function of this theory is independent of the gauge coupling. This theory flows to a superconformal fixed point in the IR, which is conjectured to be holographically dual to M-theory on AdS4 × S7/ZNf. Using the supersymmetric localization, the S3 partition function is reduced to a finite dimensional integral [19], which is dubbed the Nf matrix model in [14]. In the large N limit, the integral (2.8) can be evaluated by the saddle point approximation, where the saddle point value μ∗ of the chemical potential is given by μ∗ ≈ Plugging this value μ∗ into the perturbative part of grand potential, we recover the N 3/2 behavior of free energy.
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