# A Supersymmetric Enhancement of ${\cal N}=1$ Holographic Minimal Model

## TL;DR

This paper explores an enhancement of the ${
m N}=1$ holographic minimal model to include ${
m N}=2$ higher spin multiplets, analyzing operator product expansions and asymptotic symmetries in $AdS_3$ higher spin theory.

## Contribution

It introduces a supersymmetric extension of the ${
m N}=1$ model to ${
m N}=2$, detailing the structure of higher spin multiplets and their operator product expansions.

## Key findings

- Constructed the lowest ${
m N}=2$ higher spin multiplet at the critical level.
- Determined operator product expansions between key higher spin multiplets.
- Identified asymptotic symmetry algebra in the large $N$ limit.

## Abstract

By studying the ${\cal N}=1$ holographic minimal model at the "critical" level, we obtain the lowest ${\cal N}=2$ higher spin multiplet of spins $(\frac{3}{2}, 2, 2, \frac{5}{2})$ in terms of two adjoint fermion types for generic $N$. We subsequently determine operator product expansions between the lowest and second lowest (${\cal N}=2$) higher spin multiplet of spins $(3, \frac{7}{2}, \frac{7}{2}, 4)$, and the corresponding Vasiliev's oscillator formalism with matrix generalization on $AdS_3$ higher spin theory in the extension of $OSp(2|2)$ superconformal algebra. Under the large $N$ limit (equivalent to large central charge) in the extension of ${\cal N}=2$ superconformal algebra in two dimensions, operator product expansions provide asymptotic symmetry algebra in $AdS_3$ higher spin theory.