The Action of the (Free) $\mathcal{N} = (3,1)$ Theory in Six Spacetime Dimensions

TL;DR

This paper explicitly constructs the action for a free supersymmetric (3,1) theory in six dimensions, using prepotentials that satisfy self-duality, and verifies its supersymmetry and Poincaré invariance.

Contribution

The paper provides the first explicit formulation of the (3,1) supersymmetric action in six dimensions using prepotentials aligned with self-duality conditions.

Findings

Action is explicitly constructed and shown to be supersymmetric.

The action is first-order in time derivatives and Poincaré invariant.

Invariance under supersymmetry transformations is verified.

Abstract

The action of the free $\mathcal{N} = (3,1)$ theory in six spacetime dimensions is explicitly constructed. The variables of the variational principle are prepotentials adapted to the self-duality conditions on the fields. The $(3,1)$ supersymmetry variations are given and the invariance of the action is verified. The action is first-order in time derivatives. It is also Poincar\'e invariant but not manifestly so, just like the Hamiltonian action of more familiar relativistic field theories.