N=2 conformal gauge theories at large R-charge: the SU(N) case

Conformal theories with a global symmetry may be studied in the double scaling regime where the interaction strength is reduced while the global charge increases. Here, we study generic 4d N = 2 SU(N ) gauge theories with conformal matter content at large R-charge Q(R -> infinity) with fixed 't Hooft-like coupling kappa=QRgYM2. Our analysis concerns two distinct classes of natural scaling functions. The first is built in terms of chiral/anti-chiral two-point functions. The second involves one-point functions of chiral operators in presence of <mml:mfrac>12</mml:mfrac> -BPS Wilson-Maldacena loops. In the rank-1 SU (2) case, the two-point sector has been recently shown to be captured by an auxiliary chiral random matrix model. We extend the analysis to SU(N) theories and provide an algorithm that computes arbitrarily long perturbative expansions for all considered models, parametric in the rank. The leading and next-to-leading contributions are cross-checked by a three- loops computation in N = 1 superspace. This perturbative analysis identifies maximally non-planar Feynman diagrams as the relevant ones in the double scaling limit. In the Wilson-Maldacena sector, we obtain closed expressions for the scaling functions, valid for any rank and kappa. As an application, we analyze quantitatively the large 't Hooft coupling limit kappa >> 1 where we identify all perturbative and non-perturbative contributions. The latter are associated with heavy electric BPS states and the precise correspondence with their mass spectrum is clarified.