$1/N$ expansion of circular Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver

Abstract

Localization approach to $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circular $SU(N)$ Wilson loop $⟨\mathcal{W}⟩$. We study the subleading $1/N^2$ term in the large $N$ expansion of $⟨\mathcal{W}⟩$ at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to the ${\mathbb{Z}}_2$ orbifold of the $SU(2N)$ $\mathcal{N}=4$ SYM theory. This orbifold gauge theory should be dual to type IIB superstring in ${\mathrm{AdS}}_5\times (S^5/{\mathbb{Z}}_2)$. We present a string theory argument suggesting that the $1/N^2$ term in $⟨\mathcal{W}⟩$ in the orbifold theory should have the same strong-coupling asymptotics ${\lambda }^{3/2}$ as in the $\mathcal{N}=4$ SYM case. We support this prediction by a numerical study of the localization matrix model on the gauge theory side. We also find a relation between the $1/N^2$ term in the Wilson loop expectation value and the derivative of the free energy of the orbifold gauge theory on 4-sphere.

29 pages, several pdf figures. v3: minor corrections and note added on recent exact results in arXiv:2207.11475

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