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 $R^4/Z_2$ 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 contribute 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.