Note on SUSY BF theory in (1+2) dimensions from SUSY algebra for vector-spinor field

TL;DR

This paper demonstrates that in (1+2) dimensions, the SUSY BF action for a minimal off-shell supermultiplet is uniquely determined by the closure of the SUSY algebra, highlighting its fundamental invariance.

Contribution

It establishes the uniqueness of the SUSY BF action in (1+2) dimensions based on algebraic closure, providing a foundational understanding of SUSY invariants.

Findings

SUSY BF action is unique in (1+2) dimensions.

Closure of SUSY algebra determines the invariant action.

Supports the algebraic consistency of SUSY theories in lower dimensions.

Abstract

We show in (1+2) dimensions that supersymmetric (SUSY) BF action for a (minimal and off-shell) spin-(1,3/2) supermultiplet is a unique SUSY invariant one required from the closure property of commutator algebra for SUSY transformations.