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

TL;DR

This work constructs a nonlinear, six-dimensional theory of a chiral 2-form that reduces to a five-dimensional Born–Infeld (BI) theory for an Abelian gauge field. By promoting the 5d BI structure to a 6d equation with ${\cal F}_{\mu\nu}=F_{\mu\nu}+\partial_5 B_{\mu\nu}$ and enforcing a Lorentz-invariance constraint that becomes BI in 5d, the authors obtain a Lagrangian $S_6=\int d^6x\left(\tfrac12 \tilde{H}^{\mu\nu}\partial_5 B_{\mu\nu}+g(\tilde{H})\right)$ with $g(\tilde{H})=2(\sqrt{-\det(\eta_{\mu\nu}+i\tilde{H}_{\mu\nu})}-1)$. The paper demonstrates 6d Lorentz invariance is realized nonmanifestly and constructs a finite-tension, self-dual string soliton, highlighting the physical relevance to M-theory five-branes and D4-branes. These results provide a classical framework for six-dimensional chiral tensor theories and suggest routes toward supersymmetric and fully covariant formulations, with potential implications for nonperturbative 6d QFTs and higher-dimensional string/M-theory objects.

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.