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

## TL;DR

This paper derives explicit formulas for conformal blocks in two-dimensional $
=1$ super Liouville theory's light limit, using dualities with supersymmetric gauge theories and summing instanton series.

## Contribution

It provides the first explicit closed-form expressions for $
=1$ super Liouville conformal blocks in the light asymptotic limit, leveraging gauge theory dualities.

## Key findings

- Explicit formulas for $
=1$ super Liouville blocks in light limit.
- Identification of contributing Young diagrams in the asymptotic regime.
- Summation of instanton series to obtain closed-form expressions.

## 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.