BPS Wilson loop in $\mathcal N=2$ superconformal $SU(N)$ "orientifold" gauge theory and weak-strong coupling interpolation

Abstract

We consider the expectation value xWy of the circular BPS Wilson loop in N " 2 superconformal SU pN q gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This theory admits a regular large N expansion, is planar-equivalent to N " 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS 5 ˆS5 superstring theory. On the string theory side xWy is represented by the path integral expanded near the same AdS 2 minimal surface as in the maximally supersymmetric case. Following the string theory argument in arXiv:2007.08512, we suggest that as in the N " 4 SYM case and in the N " 2 SU pN q ˆSU pN q superconformal quiver theory discussed in arXiv:2102.07696, the coefficient of the leading non-planar 1{N 2 correction in xWy should have the universal λ 3{2 scaling at large 't Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for xWy. We complement the analytic derivation of the λ 3{2 scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Padé analysis.

Exact results in a N=2 superconformal gauge theory at strong coupling

“…It is quite remarkable that, as observed in [8], this is essentially the same matrix 6 appearing in the analysis of the zeros of Bessel functions performed in [47]. Note that the main diagonal and the super-and sub-diagonals of S converge to 0 when the size of the matrix increases.…”

“…where δ U is a non-trivial function of the 't Hooft coupling. The free energy and the vacuum expectation value of the BPS Wilson loop are examples of untwisted observables [8,22,38] but, as we will see, also the correlators of gauge invariant single-trace operators with even dimension in the E theory belong to the untwisted class.…”

“…If conformal symmetry is present 1 , this matrix model also encodes information on the observables of the theory in flat space. In this way the partition function and the vacuum expectation value of the BPS Wilson loop have been computed [1,[3][4][5][6][7][8]. Many other observables of the gauge theory can be described by the matrix model, such as the extremal correlators of chiral/anti-chiral fields [9][10][11][12][13][14][15][16][17][18][19][20][21][22], the correlators of chiral operators with the BPS Wilson loop [16,[23][24][25] and the brehmsstrahlung function [26][27][28].…”

“…If one is interested in the perturbative expansion for λ → 0, this can be efficiently generated using and so on. Evaluating these multiple integrals after expanding the Bessel functions for small λ, we have found at the first few perturbative orders that These expansions can be easily pushed to very high orders without too much computational effort and then used for numerical investigations (see also [8] for similar calculations related to the vacuum expectation value of the BPS Wilson loop).…”

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

“…The action of supersymmetric localization in N = 2 is still powerful enough to reduce the Wilson loop vacuum expectation value (vev) to a matrix model, even though it is no longer Gaussian. Several quantities have been analysed for N = 2 theories, such as the Wilson loop vev [31][32][33][34][35] together with correlators of chiral operators and Wilson loops [36][37][38] and the Bremsstrahlung function [39][40][41].…”