Nonlinear Self-Duality in Even Dimensions

TL;DR

This paper explores the duality symmetries of Born-Infeld theories with multiple fields in even dimensions, revealing new duality groups and extending the framework to real and complex fields.

Contribution

It introduces a novel auxiliary field formulation of Born-Infeld theory with n complex and real fields, uncovering the associated U(n,n) and Sp(2n,R) duality groups in even dimensions.

Findings

U(n,n) duality group for complex fields

Sp(2n,R) duality group for real fields in even dimensions

Extension of duality symmetry to arbitrary even dimensions

Abstract

We show that the Born-Infeld theory with n complex abelian gauge fields written in an auxiliary field formulation has a U(n,n) duality group. We conjecture the form of the Lagrangian obtained by eliminating the auxiliary fields and then introduce a new reality structure leading to a Born-Infeld theory with n real fields and an Sp(2n,R) duality symmetry. The real and complex constructions are extended to arbitrary even dimensions. The maximal noncompact duality group is U(n,n) for complex fields. For real fields the duality group is Sp(2n,R) if half of the dimension of space-time is even and O(n,n) if it is odd. We also discuss duality under the maximal compact subgroup, which is the self-duality group of the theory obtained by fixing the expectation value of a scalar field. Supersymmetric versions of self-dual theories in four dimensions are also discussed.