Orbifold Compactification and Solutions of M--Theory from Milne Spaces

TL;DR

This paper explores M-theory solutions derived from Milne spaces with hyperbolic geometries, analyzing orbifold identifications, spectral functions, and supersymmetry implications in eleven-dimensional supergravity.

Contribution

It introduces new solutions of M-theory using Milne spaces, details orbifold structures, and connects spectral functions with harmonic analysis on hyperbolic spaces.

Findings

Spectral functions linked to cusp forms and Eisenstein series are derived.

Orbifold identifications are analyzed in the context of hyperbolic space forms.

Supersymmetry considerations for hyperbolic space factors are briefly discussed.

Abstract

In this paper, we consider solutions and spectral functions of M-theory from Milne spaces with extra free dimensions. Conformal deformations to the metric associated with the real hyperbolic space forms are derived. For the three-dimensional case, the orbifold identifications $SL(2,{\mathbb Z}+i{\mathbb Z})/\{\pm Id\}$, where $Id$ is the identity matrix, is analyzed in detail. The spectrum of a eleven-dimensional field theory can be obtained with the help of the theory of harmonic functions in the fundamental domain of this group and it is associated with the cusp forms and the Eisenstein series. The supersymmetry surviving for supergravity solutions involving real hyperbolic space factors is briefly discussed.