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

Kavli Affiliate: Simeon Hellerman

| First 5 Authors: 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 $tau$ 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 $lambda$. We compare the expansion to exact results from
supersymmetric localization at the coupling $tau = {{25}over pi} i$, 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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