Supergravities from fields to branes

TL;DR

This paper explores supergravity theories, their classical constructions, dimensional reductions, and potential quantum and duality properties, aiming to understand their role in unifying fundamental physics.

Contribution

It reviews the classical supergravity action, analyzes dimensional reductions and their self-duality, and discusses quantum remnants and dualities beyond the massless sector.

Findings

Supergravity in 11 dimensions can be constructed via deformation of supersymmetric free theories.

Dimensional reductions exhibit a common self-duality structure.

Potential quantum remnants include U-dualities and variable spacetime dimensions.

Abstract

The quest for unification of particles and fields and for reconciliation of Quantum Mechanics and General Relativity has led us to gauge theories, string theories, supersymmetry and higher-extended objects: membranes... Our spacetime is quantum mechanical but it admits semiclassical descriptions of various ``complementary'' kinds that could be valid approximations in various circumstances. One of them might be supergravity in 11 dimensions the largest known interacting theory of a finite number of fields with gauged Poincar\' e supersymmetry. Its solitons and their dual membranes would be states in its quantum version called M-theory. We shall review the construction of its classical action by deformation of a globally supersymmetric free theory and its on-shell superspace formulation. Then we shall focus on the bosonic matter equations of the dimensional reductions on tori of dimensions 1 to 8 to exhibit their common self-duality nature. In the concluding section we shall discuss possible remnants at the quantum level and beyond the massless sector of generalised discrete U-dualities. We shall also comment on the variable dimension of spacetime descriptions and on the possibility of extending the self dual description to spacetime itself and its metric.