Shadow formalism for supersymmetric conformal blocks

TL;DR

This paper extends the shadow formalism to superconformal field theories, enabling explicit computation of superconformal blocks and verifying results against known equations in the large central charge limit.

Contribution

It introduces a generalized shadow operator construction for superconformal theories and computes explicit superconformal blocks in various settings.

Findings

Reproduces known large-c superconformal blocks on plane and torus

Explicitly derives two-point global torus superconformal block

Validates results using Casimir differential equation

Abstract

Shadow formalism is a technique in two-dimensional CFT allowing straightforward computation of conformal blocks in the limit of infinitely large central charge. We generalize the construction of shadow operator for superconformal field theories. We demonstrate that shadow formalism yields known expressions for the large-c limit of the four-point superconformal block on a plane and of the one-point superconformal block on a torus. We also explicitly find the two-point global torus superconformal block in the necklace channel and check it against the Casimir differential equation.