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

Abstract

We derive the planar limit of 2- and 3-point functions of single-trace chiral primary operators of $$ \mathcal{N} $$ N = 2 SQCD on S4, to all orders in the ’t Hooft coupling. In order to do so, we first obtain a combinatorial expression for the planar free energy of a hermitian matrix model with an infinite number of arbitrary single and double trace terms in the potential; this solution might have applications in many other contexts. We then use these results to evaluate the analogous planar correlation functions on ℝ4. Specifically, we compute all the terms with a single value of the ζ function for a few planar 2- and 3-point functions, and conjecture general formulas for these terms for all 2- and 3-point functions on ℝ4.

Strong-coupling results for $$ \mathcal{N} $$ = 2 superconformal quivers and holography

“…Localization allows one to map the partition function and other protected observables of a supersymmetric gauge theory defined on a four-sphere to quantities in a matrix model [3]; when the quantum theory is conformal, this matrix model captures also the corresponding observables in flat space. While the matrix model associated to the N = 4 SYM theory is Gaussian, the one for N = 2 theories has a complicated potential with contributions at any order in the gauge coupling constant g. Nevertheless, it can be efficiently used to study a whole set of observables, like for instance the Wilson loop vacuum expectation value [4][5][6][7], the chiral/anti-chiral correlators [8][9][10][11][12][13][14][15][16], the correlators of chiral operators and Wilson loops [17,18], as well as the Bremsstrahlung function [19][20][21][22].…”

On the planar free energy of matrix models

“…The second ingredient, which builds upon the first, is a recently found combinatorial expression for the planar free energy of matrix models with potentials of the form (1.2) [7,9] as a sum over a particular type of graphs, known as tree graphs…”

“…Let's explain the content of this expression (see [7,9] for the derivation and further details). At a given order m, (1.7) instructs us to consider all tree diagrams (i.e.…”

“…Once we have distributed all operators among the vertices of the tree according to these rules, the contribution of each vertex is given by the planar connected correlator of its operators, given by (1.5). While in this work we will focus on the planar free energy, we have shown in previous work how to apply this approach to the planar limit of other observables, like the Wilson loop [7,8] or extremal correlators [9].…”

“…On the other hand, potentials of the form (1.2) with an infinite number of terms appear in statistical physics, in Chern-Simons theories with matter, or in duals to M-theory on certain JHEP02(2022)078 backgrounds as reviewed in [5]. More recently, it has been realized [6][7][8][9] that supersymmetric localization [10] reduces the evaluation of certain observables of four dimensional N " 2 super Yang-Mills (SYM) theories on S 4 to matrix models that can be recast to take the form of (1.2). One of the basic objects of interest in the study of these matrix models is the free energy F " F ´Fgaussian " log Z " log Z ´log Z gaussian (1.3) and since the groundbreaking work [11] it has been understood that one can organize the perturbative evaluations of the free energy in a double series expansion…”