Aspects of Born-Infeld Theory and String/M-Theory

TL;DR

This work provides a concise, geometry-centric survey of Born-Infeld theory and its string/M-theory realizations, focusing on causality, energy conditions, and the distinct open-string vs closed-string metrics that govern brane dynamics. It develops the Dirac-Born-Infeld framework, analyzes BIon-type and BPS solutions, and explores the causal structure via Boillat cones and Hooke's law, connecting to open-string equivalence principles and finite-temperature effects like the Tolman redshift of the Hagedorn limit. The text then delves into strong-coupling regimes, including Weyl-invariant and string-fluid limits, auxiliary-field formulations, and tachyon condensation, before extending these ideas to the M5-brane with non-linear self-duality and related Boillat/Hooke structures. The overall thrust is to illuminate how geometric and thermodynamic considerations constrain the nonlinear dynamics of branes and their dualities, with implications for tachyon condensation, extreme solutions, and high-field limits in string/M-theory.

Abstract

These notes provide a hopefully pedagogic introduction to Born-Infeld theory and some of its uses in String/M-Theory from the perspective of some-one interested in spacetime geometry. Causality and the consequences of having both the open string and closed string metric are stressed. This leads to some new insighst into old problems, such as strings at finite temperature. Various strong coupling limits of both Born-Infeld and the M5-brane theories are described and their relevance for tachyon condensations are mentioned.