$\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators

TL;DR

This paper derives new superconformal blocks for 4d $ =1$ SCFTs using supershadow methods, generalizing previous results for special cases like chiral operators and conserved currents.

Contribution

It introduces a general framework for superconformal blocks involving arbitrary scalar operators with any dimension and R-charge, extending prior specific cases.

Findings

Derived new superconformal block expressions for general scalar operators.

Unified previous special cases like chiral and conserved current blocks.

Provided explicit formulas for four-point functions with neutral R-symmetry exchange.

Abstract

We use supershadow methods to derive new expressions for superconformal blocks in 4d $\mathcal{N}=1$ superconformal field theories. We analyze the four-point function $\langle\mathcal{A}_1 \mathcal{A}_2^\dagger \mathcal{B}_1 \mathcal{B}_2^\dagger\rangle$, where $\mathcal{A}_i$ and $\mathcal{B}_i$ are scalar superconformal primary operators with arbitrary dimension and $R$-charge and the exchanged operator is neutral under $R$-symmetry. Previously studied superconformal blocks for chiral operators and conserved currents are special cases of our general results.