The light asymptotic limit of conformal blocks in mathcal{N}=1 super Liouville field theory

Abstract

Analytic expressions for the two dimensional mathcal{N}=1 SLFT blocks in the light semi-classical limit are found for both Neveu-Schwarz and Ramond sectors. The calculations are done by using the duality between SU(2) mathcal{N}=2 super-symmetric gauge theories living on R4/Z2 space and two dimensional mathcal{N}=1 super Liouville field theory. It is shown that in the light asymptotic limit only a restricted set of Young diagrams contributes to the partition function. This enables us to sum up the instanton series explicitly and find closed expressions for the corresponding mathcal{N}=1 SLFT four point blocks in the light asymptotic limit.