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

Abstract Analytic expressions for the two dimensional N = 1 $$ \mathcal{N}=1 $$ 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) N = 2 $$ \mathcal{N}=2 $$ super-symmetric gauge theories living on R 4 /Z 2 space and two dimensional N = 1 $$ \mathcal{N}=1 $$ 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 N = 1 $$ \mathcal{N}=1 $$ SLFT four point blocks in the light asymptotic limit.