Towards the Realization of the Dark Dimension Scenario in Ho\v{r}ava-Witten Theory

TL;DR

This paper explores how Hořava-Witten theory could realize the Dark Dimension Scenario, addressing issues like proton decay and linking moduli dependence of physical constants to one-loop integrals over state towers.

Contribution

It proposes a new approach using symmetric tadpole cancellation and infinite distance limits to connect Hořava-Witten theory with the Dark Dimension Scenario and M-theoretic ideas.

Findings

Symmetric tadpole cancellation may mitigate proton decay issues.

A special infinite distance limit is identified in the theory.

Speculation on deriving physical constants from one-loop integrals over towers of states.

Abstract

It has been suggested that Ho\v{r}ava-Witten theory could provide a concrete realization of the Dark Dimension Scenario. In this context, the observable Standard Model sector is naturally localized in the micron-sized large dimension, which is the interval in the eleventh direction. Considering Calabi-Yau manifolds supporting generic vector bundles including also abelian factors, we point out that symmetric tadpole cancellation on the $E_8$ walls has the potential to ameliorate some of the issues of such a realization, including too fast proton decay. By taking not only the hierarchically small value of the dark energy but also the size of the Standard Model gauge couplings into account, one is driven to a special infinite distance limit, which is the Ho\v{r}ava-Witten analogue of a limit recently at the focus of the M-theoretic Emergence Proposal. Extrapolating results obtained for BPS-saturated amplitudes, we speculate about the possibility of obtaining the moduli dependence of the scalar potential, the gauge couplings and the Planck scale by simple one-loop Schwinger integrals over towers of states.