# Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry

## TL;DR

This paper derives superconformal blocks for mixed 1/2-BPS correlators in 4D SCFTs with SU(2) R-symmetry, using Casimir equations and Ward identities to express them in terms of bosonic blocks.

## Contribution

It provides a systematic, dimension-independent method to determine superconformal blocks for mixed BPS correlators with SU(2) R-symmetry, revealing relations among coefficients.

## Key findings

- Explicit superconformal blocks expressed in bosonic terms
- Coefficients related through linear transformations
- Method applicable to various dimensions

## Abstract

For SCFTs with an $SU(2)$ R-symmetry, we determine the superconformal blocks that contribute to the four-point correlation function of a priori distinct half-BPS superconformal primaries as an expansion in terms of the relevant bosonic conformal blocks. This is achieved by using the superconformal Casimir equation and the superconformal Ward identity to fix the coefficients of the bosonic blocks uniquely in a dimension-independent way. In addition we find that many of the resulting coefficients are related through a web of linear transformations of the conformal data.