Interacting Chiral Gauge Fields in Six Dimensions and Born-Infeld Theory

TL;DR

This paper explores the dimensional reduction of 6d self-dual tensor gauge fields to 5d Abelian gauge fields, deriving conditions for Lorentz invariance and formulating the 6d theory that yields 5d Born-Infeld theory, including soliton solutions.

Contribution

It establishes the conditions for 5d Abelian gauge theories to originate from 6d self-dual tensor theories and formulates a manifestly Lorentz-invariant 6d theory for Born-Infeld dynamics.

Findings

Derived conditions for dimensional reduction from 6d to 5d gauge theories.

Formulated a 6d Lorentz-invariant theory for Born-Infeld fields.

Constructed a string soliton with finite tension and self-dual charge.

Abstract

Dimensional reduction of a self-dual tensor gauge field in 6d gives an Abelian vector gauge field in 5d. We derive the conditions under which an interacting 5d theory of an Abelian vector gauge field is the dimensional reduction of a 6d Lorentz invariant interacting theory of a self-dual tensor. Then we specialize to the particular 6d theory that gives 5d Born-Infeld theory. The field equation and Lagrangian of this 6d theory are formulated with manifest 5d Lorentz invariance, while the remaining Lorentz symmetries are realized nontrivially. A string soliton with finite tension and self-dual charge is constructed.