Emergent spacetime and black hole probes from automorphic forms

TL;DR

This paper explores how automorphic forms from the Langlands program can be used to understand emergent spacetime geometry and black hole probes in string theory, linking advanced mathematics with fundamental physics.

Contribution

It introduces novel applications of automorphic forms to derive spacetime geometry and analyze black holes within string theory frameworks.

Findings

Automorphic forms can encode spacetime geometry in string theory.

Automorphic black holes serve as probes of spacetime structure.

The Langlands program connects number theory with fundamental physics.

Abstract

Over the past few years the arithmetic Langlands program has found applications in two quite different problems that arise in string physics. The first of these is concerned with the fundamental problem of deriving the geometry of spacetime from the worldsheet dynamics, leading to a realization of the notion of an emergent spacetime in string theory. The second problem is concerned with the idea of using automorphic black holes as probes of spacetime. In this article both of these applications of the Langlands program are described.