Large R-charge EFT correlators in N=2 SQCD

Abstract

We consider large-R-charge Coulomb branch correlation functions in N = 2 superconformal QCD in D=4 dimensions, with gauge group G = SU (2) and N F = 4 hypermultiplets in the fundamental representation. Using information from supersymmetric recursion relations, S−duality, and matching of EFT parameters with the doublescaling limit, we give an exact formula for the massless Coulomb branch EFT contribution to the correlation function two-point functions of the n th power of the chiral ring generator, G τ ] , with A[τ ] and B[τ ] given as explicit functions of the coupling constant τ in closed form. We note the precise agreement of the EFT formula with supersymmetric localization even at low values of n, and discuss aspects of the post-EFT remainder contributed by the macroscopic virtual propagation of massive particles.

On the exponentially small corrections to ${\cal N} = 2$ superconformal correlators at large R-charge

“…One particularly nice testing ground for these ideas has been superconformal field theory in D = 4 with N = 2 extended supersymmetry. [5][6][7][8][9][10][11][12][13], particularly those with a one-complex-dimensional Coulomb branch. For such theories there are tools available associated with exact supersymmetry that allow the computation of supersymmetricallyprotected observables at a nonperturbative level, with the computation of the S 4 partition function as a starting point.…”

“…For the special case of rank-one gauge group G = SU (2), the chiral ring of the Coulomb branch is generated by a single operator O ∆ of dimension ∆ and U (1) R R-charge 2 J = ∆. In previous work [5][6][7][8] the correlation functions of the n th powers of these operators have been computed in a large-n expansion. In the expansion at large n with the coupling held fixed, there is a simple asymptotic formula for the 1 The formal description of the Abelian large-charge eft in terms of the NG degrees of freedom via the CCWZ formalism [78,79]was explored in [16].…”

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In this note we consider Coulomb-branch chiral primary correlation functions in N = 2 superconformal QCD with gauge group SU (2), in the limit of large R-charge J = 2n for the chiral primary operators [O(x)] n with the inverse gauge coupling τ held fixed. In previous work [5][6][7][8] these correlation functions were determined to all orders in n, up to unknown exponentially small corrections. In this paper we determine the first several orders of the asymptotic expansion of the exponentially small correction itself.

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The Breakdown of Resummed Perturbation Theory at High Energies

“…For a recent assessment see also [19,20]. 2 Recently, semiclassical expansions in parameters of the form λn have also proven useful in quantum theories for the investigation of physical quantities at large quantum numbers, see, e.g., [27][28][29][30][31][32][33][34][35][36][37][38][39][40]. 3 For theories featuring a spontaneously broken symmetry the situation is more complicated, as the first quantum correction to the exponent is positive [7,9,10].…”

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

“…More recently, it has been shown [6,7] that the evaluation of closely related n-point 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].…”