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

Abstract

Localization approach to N " 2 superconformal SU pN q ˆSU pN q quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circular SU pN q Wilson loop xWy. We study the subleading 1{N 2 term in the large N expansion of xWy at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to the Z 2 orbifold of the SU p2N q N " 4 SYM theory. This orbifold gauge theory should be dual to type IIB superstring in AdS 5 ˆpS 5 {Z 2 q. We present a string theory argument suggesting that the 1{N 2 term in xWy in the orbifold theory should have the same strong-coupling asymptotics λ 3{2 as in the N " 4 SYM case. We support this prediction on the gauge theory side by a numerical study of the localization matrix model. 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.

Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers

“…The same happens for correlators of multiple coincident Wilson loops, which coincide with the N = 4 analogue in the planar limit, see equation (4.31). These facts confirm at weak coupling a well known holographic result [55,57,58,61], since the minimal surface described by the Wilson loop is unaffected by the orbifold Z q . See also section 4.4 for additional comments about Wilson loop vevs for AdS/CF T perspectives.…”

“…A q−1 theories also admit a localization approach that localizes observables on a multi-matrix model. Many results have been recently obtained using such matrix model, in particular for Wilson loop vevs [55][56][57][58] and for chiral/antichiral correlators [1,59]. In [1] a complete analysis of A q−1 matrix model has been developed and applied to the two-point correlators of chiral/anti-chiral operators, by solving the mixing problem in moving from the flat space to S 4 and finding general formulas for the two-point chiral correlators for any values of the dimension n and the number of vector multiplets q.…”

“…In[34,38,54,55] a special N = 2 SCFT with symmetric and antisymmetric matter content has been considered, and such theory also enjoys nice holographic properties. It would be very interesting to fully understand the common properties shared with Aq−1 theories.…”

Integrated correlators at strong coupling in an orbifold of $$ \mathcal{N} $$ = 4 SYM

“…This is the most symmetric configuration and possesses a known holographic dual given by Type II B string theory on a space-time of the type AdS 5 ×S 5 /Z 2 [58,59]. Over the last few years, many BPS-observables in the large-N limit of this superconformal theory have been examined, both at weak and strong-coupling, exploting supersymmetric localization techniques, such as the free energy and the VEV of one or more circular Wilson loops [60][61][62][63][64][65][66][67] and the 2-and 3point functions of chiral/anti-chiral primary operators [13,16,18,19,[22][23][24]26].…”