Hyperbolic Space Forms and Orbifold Compactification in M-Theory

TL;DR

This paper explores hyperbolic space solutions in string theory and supergravity, focusing on compactifications, fluxes, and supersymmetry, with implications for holography and conformal field theories.

Contribution

It provides new examples of hyperbolic space compactifications, analyzes their fluxes and symmetries, and discusses supersymmetry and holographic principles in these contexts.

Findings

Hyperbolic coset spaces enable novel string compactifications.

Finite flux and tensor kernels are characterized for hyperbolic spaces.

Supersymmetry can survive in certain hyperbolic space configurations.

Abstract

We analyze solutions of string theory and supergravity which involve real hyperbolic spaces. Examples of string compactifications are given in terms of hyperbolic coset spaces of finite volume $\Gamma\backslash {\mathbb H}^N$, where $\Gamma$ is a discrete group of isometries of ${\mathbb H}^N$. We describe finite flux and the tensor kernel associated with hyperbolic spaces. The case of arithmetic geometry of $\Gamma = SL(2, {\mathbb Z}+i{\mathbb Z})/\{\pm Id\}$, where $Id$ is the identity matrix, is analyzed. We discuss supersymmetry surviving for supergravity solutions involving real hyperbolic space factors, string-supergravity correspondence and holography principle for a class of conformal field theories.