Duality Covariant Solutions in Extended Field Theories

TL;DR

This paper explores duality covariant solutions in extended field theories like double and exceptional field theory, unifying supergravity fields and revealing dualities through extended geometries and solutions such as waves and monopoles.

Contribution

It introduces solutions to extended field theory equations, analyzes their properties, and links isometries to duality relations, also connecting exceptional field theory to F-theory.

Findings

Solutions include waves and monopoles in extended space

Isometries generate duality relations between supergravity solutions

Established connection between exceptional field theory and F-theory

Abstract

Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to winding modes of the fundamental objects. This geometrically unifies the spacetime metric and the gauge fields (and their local symmetries) in a generalized geometry. Solutions to these extended field theories take the simple form of waves and monopoles in the extended space. From a supergravity point of view they appear as 1/2 BPS objects such as the string, the membrane and the fivebrane in ordinary spacetime. In this thesis double field theory and exceptional field theory are introduced, solutions to their equations of motion are constructed and their properties are analyzed. Further it is established how isometries in the extended space give rise to duality relations between the supergravity solutions. Extensions to these core ideas include studying Goldstone modes, probing singularities at the core of solutions and localizing them in winding space. The relation of exceptional field theory to F-theory is also covered providing an action for the latter and incorporating the duality between M-theory and F-theory.