Toroidal $\&$ orbifold compactifications at large D and D-duality

TL;DR

This paper explores the behavior of quantum gravity and string theories in large dimensions, focusing on orbifold volumes, mass spectra, and the potential for a D-duality symmetry relating different compactifications.

Contribution

It introduces the concept of D-duality in higher-dimensional gravity and investigates its restrictions within string theory, providing specific duality examples involving orbifolds and S-folds.

Findings

Volumes of certain orbifolds shrink at large D

KK modes become heavy, wrapped branes become light at large D

D-duality relates different gravity compactifications

Abstract

In this paper I will further investigate the spectrum of quantum gravity or string theories at large number of dimensions. We will see that volumes of certain orbifolds shrink at large D. It follows that the mass spectra of the leading Kaluza-Klein towers and also of wrapped brane states on these orbifolds possess a non-trivial dependence on D: KK modes become heavy at large D, whereas wrapped branes become light. This observation can be used either to apply the Large Dimension Conjecture or, as we will do, to investigate the possibility of a D-duality symmetry, which relates in gravity compactifications of different dimensions. We will set up the general rules for D-duality in higher dimensional gravity. However due to existence of the critical dimensions, D-duality is quite restricted in string theory. As simple tests for D-duality in string theory, we will discuss the duality between M-theory on a two-dimensional orbifold, namely the M\"obius strip, and an IIB S-fold on a circle, which corresponds to the heterotic CHL string, as well the duality between a (truncated) 12-dimensional theory on a three-dimensional orbifold and another IIB S-fold compactification. Finally I also comment on the possible existence of exotic theories at large D.