Exact results in a $$ \mathcal{N} $$ = 2 superconformal gauge theory at strong coupling

Abstract

We consider the $$ \mathcal{N} $$ N = 2 SYM theory with gauge group SU(N) and a matter content consisting of one multiplet in the symmetric and one in the anti-symmetric representation. This conformal theory admits a large-N ’t Hooft expansion and is dual to a particular orientifold of AdS5 × S5. We analyze this gauge theory relying on the matrix model provided by localization à la Pestun. Even though this matrix model has very non-trivial interactions, by exploiting the full Lie algebra approach to the matrix integration, we show that a large class of observables can be expressed in a closed form in terms of an infinite matrix depending on the ’t Hooft coupling λ. These exact expressions can be used to generate the perturbative expansions at high orders in a very efficient way, and also to study analytically the leading behavior at strong coupling. We successfully compare these predictions to a direct Monte Carlo numerical evaluation of the matrix integral and to the Padé resummations derived from very long perturbative series, that turn out to be extremely stable beyond the convergence disk |λ| < π2 of the latter.

The planar limit of $$ \mathcal{N} $$ = 2 chiral correlators

“…The path described above has been followed already in a number of papers [3][4][5][8][9][10][11][12][13]. The novel ingredient that we introduce in this work is an alternative way of evaluating the free energy and correlators of the relevant matrix models, which allows us to obtain allorder analytic expressions in the planar limit.…”

“…In this work, we have focused on the terms with maximal transcendality; it might be possible to find analytic formulas for the coefficients of ofher terms with simple patterns, like those with just powers of ζ 3 , as in [29]. It should also be possible to extend the analysis presented here for N " 2 SCQD to extremal correlators of other Lagrangian N " 2 SCFTs [11][12][13]30]. A very interesting problem would be to prove our conjectures (1.4) and (1.5).…”

“…These ingredients hint at a diagrammatic derivation of (4.10). Finally, let us mention that [11,13] have developed very efficient techniques to obtain analytic results for certain N " 2 SCFTs, which currently don't include N " 2 SCQD. In these works, a crucial role is played by an infinite matrix that can be written as an integral over Bessel functions.…”

“…It would be interesting to extend the techniques of [11,13] to arbitrary N " 2 Lagrangian SCFTs; this would allow to prove (4.10) and extend it to terms with two or more values of ζ.…”

“…A first approach [2][3][4][5] uses a 4d analog of the tte quations [1]. More recently, it has been shown [6,7] that the evaluation of closely related npoint functions on S 4 can be reduced through supersymmetric localization to matrix model computations; in turn, a Gram-Schmidt orthogonalization procedure applied to these S 4 correlators yields the correlators on R 4 [8][9][10][11][12][13]. Alternatively, the large R-charge limit [14] of these correlation functions has been studied in [15][16][17][18][19][20].…”