# Component $d=6$ Born-Infeld theory with $N=(2,0)\rightarrow N=(1,0)$ supersymmetry breaking

## TL;DR

This paper constructs a $d=6$, $N=(1,0)$ supersymmetric Born-Infeld theory with partial supersymmetry breaking, extending known $d=4$ results and demonstrating its reduction to a self-dual $N=4$, $d=4$ theory.

## Contribution

It develops a formalism for $d=6$, $N=(1,0)$ Born-Infeld theory with partial supersymmetry breaking, including invariance conditions and reduction to four dimensions.

## Key findings

- Constructed a $d=6$, $N=(1,0)$ supersymmetric Born-Infeld action.
- Demonstrated invariance under unbroken supersymmetry in lowest order.
- Reduced the $d=6$ theory to a self-dual $N=4$, $d=4$ Born-Infeld theory.

## Abstract

The formalism of nonlinear realizations is used to construct a theory with $1/2$ partial breaking of global supersymmetry with the $N=(1,0)$, $d=6$ abelian vector multiplet as a Goldstone superfield. Much like the case of the $N=2$, $d=4$ Born-Infeld theory, proper irreducibility conditions of the multiplet are selected by the invariance with respect to the external automorphisms of the Poincar\'e superalgebra. They are found in the lowest nontrivial order in the auxiliary field. The fermionic contributions to the Bianchi identity are restored by assuming its covariance with respect to broken supersymmetry. The invariance of the action with respect to unbroken supersymmetry is checked in the lowest order in the fermionic fields. The supersymmetry preserving reduction of the $d=6$ action to four dimensions is performed, resulting in the $N=4$, $d=4$ Born-Infeld theory. As expected, the reduced action enjoys $U(1)$ self-duality.