The Two-Parameter Brane Sigma-Model: M*, M' solutions and M-theory solutions dependent on exotic coordinates

TL;DR

This paper explores two-parameter sigma-model solutions within E11 that lead to novel M* and M'-theory space-time solutions with metrics depending on general wave functions, extending traditional harmonic function solutions.

Contribution

It introduces a new class of solutions in M-theory derived from two-parameter sigma-models on symmetric spaces within E11, incorporating dependence on exotic coordinates.

Findings

Solutions depend on general wave functions, not harmonic functions.

Weyl reflection maps these solutions to standard M-theory solutions.

Metrics involve exotic coordinates from E11's fundamental representation.

Abstract

We investigate two-parameter solutions of sigma-models on two dimensional symmetric spaces contained in E11. Embedding such sigma-model solutions in space-time gives solutions of M* and M'-theory where the metric depends on general travelling wave functions, as opposed to harmonic functions typical in general relativity, supergravity and M-theory. Weyl reflection allows such solutions to be mapped to M-theory solutions where the wave functions depend explicitly on extra coordinates contained in the fundamental representation of E11.