Particle actions and brane tensions from double and exceptional geometry

TL;DR

This paper develops a unified particle action framework within double and exceptional field theories to explain the origin of mass and tension in string/M-theory, connecting higher-dimensional symmetries with lower-dimensional massive particles and branes.

Contribution

It introduces a novel particle action invariant under generalized diffeomorphisms, linking extended spacetime symmetries to particle masses, brane tensions, and the Romans mass in string theory.

Findings

Provides a higher-dimensional perspective on mass and tension in string/M-theory.

Derives the D0 brane action in massive IIA from exceptional field theory.

Shows the role of an extra vector field in worldline actions for invariance.

Abstract

Massless particles in $n+1$ dimensions lead to massive particles in $n$ dimensions on Kaluza-Klein reduction. In string theory, wrapped branes lead to multiplets of massive particles in $n$ dimensions, in representations of a duality group $G$. By encoding the masses of these particles in auxiliary worldline scalars, also transforming under $G$, we write an action which resembles that for a massless particle on an extended spacetime. We associate this extended spacetime with that appearing in double field theory and exceptional field theory, and formulate a version of the action which is invariant under the generalised diffeomorphism symmetry of these theories. This provides a higher-dimensional perspective on the origin of mass and tension in string theory and M-theory. Finally, we consider the reduction of exceptional field theory on a twisted torus, which is known to give the massive IIA theory of Romans. In this case, our particle action leads naturally to the action for a D0 brane in massive IIA. Here an extra vector field is present on the worldline, whose origin in exceptional field theory is a vector field introduced to ensure invariance under generalised diffeomorphisms.