$$ \mathcal{N} $$ = 2 conformal gauge theories at large R-charge: the SU(N) case

Abstract

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 → ∞ with fixed 't Hooft-like coupling κ = Q R g 2 YM . 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 1 2 -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 κ. As an application, we analyze quantitatively the large 't Hooft coupling limit κ 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. arXiv:2001.06645v2 [hep-th] 28 Jan 20201 The idea of a large charge/weak coupling compensation is closely related to the solvability of the BMN limit in AdS/CFT [4,5] and, more generally, to the coherent-state effective theory description of "semiclassical" string states [6,7] and its role in capturing the strong coupling regime [8].2 An equivalent statement is that an exact saddle point analysis is possible in the double scaling limit.

Resurgence of the large-charge expansion

“…The same geometric picture also appears in the case of supersymmetric systems. For example, in N = 2 sqcd at large R-charge similar non-perturbative contributions were discussed numerically [15][16][17] and analytically in the double scaling limit in [18][19][20][21] and were found to be consistent with the propagation of massive hypermultiplets around geodesics.…”

On the UV completion of the O(N) model in 6 − ϵ dimensions: a stable large-charge sector

“…The existence of this double scaling limit was first hinted for scalar theories long ago in [41][42][43], and very recently reconsidered in [40,[44][45][46]. Even though these studies concern scalar theories (mostly the O(2) model), a similar double-scaling limit was found in N = 2 SQCD in [47] and further studied in [48][49][50][51] (see also [52,53]). It is very interesting to note that in the large n limit of N = 2 QCD the (Yang-Mills) instanton sector is exponentially suppressed [47] and thus the perturbative series (or, if summed, its continuation to strong coupling) is exact.…”

$$ \mathcal{N} $$ = 2 Conformal SYM theories at large $$ \mathcal{N} $$

“…These techniques are very efficient in the perturbative regime at finite N . They allow to explore different sectors of the gauge theory [43][44][45][46][47][48] and can be used also in non-conformal cases [20]. Similar methods have been used also in [39,49].…”