Particle actions and brane tensions from double and exceptional geometry

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.

36 pages plus appendices, v2: typos, minor clarifications etc, v3: ditto, v4: corrected accidental use of D instead of n in the definitions of the generalised fluxes

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Cited by in corpus (12)

• The Geometry, Branes and Applications of Exceptional Field Theory
• Einstein Double Field Equations
• Non-Riemannian geometry of M-theory
• Five-brane actions in double field theory
• The Exceptional Sigma Model
• Exceptional M-brane sigma models and $\eta$-symbols
• Type II strings are Exceptional
• O-folds: Orientifolds and Orbifolds in Exceptional Field Theory
• Stringy Gravity: Solving the Dark Problems at `short' distance
• Stringy Newton Gravity with $H$-flux
• Perturbations in $\mathbf{O}(D,D)$ string cosmology from double field theory
• Lagrangian formulation for electric charge in a magnetic monopole distribution