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

Abstract

We consider the expectation value $$ \left\langle \mathcal{W}\right\rangle $$ W of the circular BPS Wilson loop in $$ \mathcal{N} $$ N = 2 superconformal SU(N) 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 $$ \mathcal{N} $$ N = 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS5× S5 superstring theory. On the string theory side $$ \left\langle \mathcal{W}\right\rangle $$ W is represented by the path integral expanded near the same AdS2 minimal surface as in the maximally supersymmetric case. Following the string theory argument in [5], we suggest that as in the $$ \mathcal{N} $$ N = 4 SYM case and in the $$ \mathcal{N} $$ N = 2 SU(N) × SU(N) superconformal quiver theory discussed in [19], the coefficient of the leading non-planar 1/N2 correction in $$ \left\langle \mathcal{W}\right\rangle $$ W should have the universal λ3/2 scaling at large ’t Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for $$ \left\langle \mathcal{W}\right\rangle $$ W . We complement the analytic derivation of the λ3/2 scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Padé analysis.

Exact results in a $$ \mathcal{N} $$ = 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 [50]. 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 [8,22,39] 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. In the N = 4 theory there are observables, which we call T 0 , that in the holographic correspondence are mapped to supergravity excitations of AdS 5 × S 5 which are odd under the Z 2 orbifold/orientifold parity.…”

“…If conformal JHEP07(2021)185 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/antichiral 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][29].…”

“…These expressions contain the exact dependence on λ since the free energy F can be written in closed form in terms of the matrix X as we have seen in (3.18). If one is interested in the perturbative expansion for λ → 0, this can be efficiently generated using 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).…”

“…In section 3.3 we showed that, in the large-N limit, the correlators of even traces have a simple expression in terms of the free energy F given in (3.48). The strong coupling behavior of the free energy has been recently studied in [8], where it has been found that…”