Supersymmetric Galilean conformal blocks

TL;DR

This paper develops the bootstrap framework for supersymmetric Galilean Conformal field theories in two dimensions, deriving explicit blocks and equations for $ ext{N}=1$ and $ ext{N}=2$ cases, with potential applications in flat holography.

Contribution

It constructs the supersymmetric Galilean conformal blocks for $ ext{N}=1$ and $ ext{N}=2$ extensions and derives bootstrap equations based on crossing symmetry.

Findings

Global SGC blocks match large central charge limit

Bootstrap equations formulated for $ ext{N}=1$ and $ ext{N}=2$ cases

Analytic solutions to Casimir differential equations obtained

Abstract

We set up the bootstrap procedure for supersymmetric Galilean Conformal (SGC) field theories in two dimensions by constructing the SGC blocks in the $\mathcal{N}=1$ and two possible $\mathcal{N} =2$ extensions of the Galilean conformal algebra. In all analyzed cases, we present the bootstrap equations by crossing symmetry of the four point function. In addition, we compute the global SGC blocks analytically by solving the differential equations obtained by acting with the Casimirs of the global subalgebras inside the four point function. These global blocks agree with the general SGC blocks in the limit of large central charge. We comment on possible applications to supersymmetric BMS$_3$ invariant field theories and flat holography.