Abstract
AbstractIn 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 Möbius 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.
Highlights
In this paper I will further investigate the spectrum of quantum gravity or string theories at large number of dimensions
E.g. the type II A superstring in 10 space-time dimensions theory was shown to be equivalent to 11-dimensional M-theory [12] and 10-dimensional IIB superstring theory can be formulated in terms of F-theory [13], which possesses several features of a 12-dimensional theory
The proposed Large-D Conjecture (LDC), together with a negative distance conjecture (NDC) state that ∆(D) for certain towers of states should stay positive as a function of the number of space-time dimensions, unless there is a dual tower of states at large space-time dimensions
Summary
We recall briefly some of the main aspects of the Large Dimension Conjecture, which was introduced in [23]. (iii) For a tower with negative ∆i, the effective Planck mass MP(d) in d dimensions becomes smaller than the fundamental Planck mass MP(D) or becomes smaller than the string scale Ms, which means the effective gravity theory becomes strongly coupled at energies lower than MP(d) These are three circumstances, which should not happen in a well defined and controllable EFT for quantum gravity, unless there is a weakly coupled dual tower of states, with m < MP and gi < 1. Having introduced D as swampland parameter, the Large Distance Conjecture (LDC) can be formulated as an extension of the NDC: If there is a leading tower of states |i with a non-trivial D-dependence, the corresponding distance must be a positive function of the EFT fields φ and of the number of dimensions D,. In the following we will further discuss the KK spectrum of tori and certain orbifolds at large D and how D-duality symmetries can be possibly realized
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