Abstract
We present a prototype for Wilsonian analysis of asymptotics of supersymmetric partition functions of non-abelian gauge theories. Localization allows expressing such partition functions as an integral over a BPS moduli space. When the limit of interest introduces a scale hierarchy in the problem, asymptotics of the partition function is obtained in the Wilsonian approach by i) decomposing (in some suitable scheme) the BPS moduli space into various patches according to the set of light fields (lighter than the scheme dependent cut-off Λ) they support, ii) localizing the partition function of the effective field theory on each patch (with cut-offs set by the scheme), and iii) summing up the contributions of all patches to obtain the final asymptotic result (which is scheme-independent and accurate as Λ → ∞). Our prototype concerns the Cardy-like asymptotics of the 4d superconformal index, which has been of interest recently for its application to black hole microstate counting in AdS5/CFT4. As a byproduct of our analysis we obtain the most general asymptotic expression for the index of gauge theories in the Cardy-like limit, encompassing and extending all previous results.
Highlights
Direction, following in the footsteps of Di Pietro, Honda, and Komargodski [5, 6]
We present a prototype for Wilsonian analysis of asymptotics of supersymmetric partition functions of non-abelian gauge theories
When the limit of interest introduces a scale hierarchy in the problem, asymptotics of the partition function is obtained in the Wilsonian approach by i) decomposing the BPS moduli space into various patches according to the set of light fields they support, ii) localizing the partition function of the effective field theory on each patch, and iii) summing up the contributions of all patches to obtain the final asymptotic result
Summary
Throughout this work the symbol means that the ratio of the two sides is 1, up to exponentially suppressed error of the form O(e−1/β). If there is dependence on extra parameters xj, we say A(β, xj) B(β, xj) uniformly over a certain domain, if there is a c > 0 that works as above While finalizing this manuscript we learned of work by A. Cabo-Bizet [59] using a decomposition method to study Cardy-like asymptotics of 4d superconformal indices
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