Kavli Affiliate: Simeon Hellerman
| Summary:
In this note we consider Coulomb-branch chiral primary correlation functions in $cal N = 2$ superconformal QCD with gauge group $SU(2)$, in the limit of large R-charge $cal J = 2n$ for the chiral primary operators $[cal O(x)]^ n$ with the inverse gauge coupling $τ$ held fixed. In previous work, 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. To do this we use: the physical interpretation of the exponentially small correction as the virtual propagation of a massive BPS particle, to fix the leading term in the expansion; the supersymmetric recursion relations to derive differential equations for the coupling-dependence of the subleading terms; and the double-scaling limit, to fix undetermined coefficients in the solution of the differential equation. We calculate the expansion of the exponentially small term up to and including relative order $n^-5over 2$. We also use the recursion relations to calculate the subleading large-$cal J$ corrections to the exponentially small correction in the double-scaling limit, up to and including relative order $n^-5$ at fixed double-scaled coupling $λ$. We compare the expansion to exact results from supersymmetric localization at the coupling $τ= 25over π i$, up to $n=150$. At values $nsim 100-150$, we find the fixed-coupling and double-scaled large-R-charge expansions are accurate to within one part in $10^ 6$ and $10^ 8$, respectively, of the size of the exponentially small correction itself. Relative to the full correlator including the dominant EFT contribution, these estimates give results accuracte to one part in $10^15$ and $10^17$, respectively.
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