Dynamical Cobordism of a Domain Wall and its Companion Defect 7-brane

TL;DR

This paper investigates the dynamical effects of non-supersymmetric domain walls in string theory, revealing that singularities suggest the necessity of a new 7-brane defect, described by novel non-isotropic solutions to the equations of motion.

Contribution

It introduces a new class of non-isotropic solutions to dilaton-gravity equations that model end-of-the-world 7-branes associated with non-supersymmetric domain walls.

Findings

Singularities imply the need for a defect, consistent with the cobordism conjecture.

A new non-isotropic solution describes the end-of-the-world 7-brane.

The solution is closely related to the initial domain wall configuration.

Abstract

Starting from an already known solution in the literature, we study the dynamical cobordism induced by the backreaction of a non-supersymmetric, positive tension domain wall in string theory. This could e.g. be a non-BPS D8-brane of type I or a $\overline{D8}/O8$ stack of a non-supersymmetric type IIA orientifold. The singularities which typically appear indicate either an inherent inconsistency of this background or the required presence of a suitable defect, as predicted by the cobordism conjecture. We provide evidence that this end-of-the-world $7$-brane is explicitly described by a new kind of non-isotropic solution of the dilaton-gravity equations of motion. Intriguingly, on the formal level this solution turns out to be closely related to the initial solution for the non-supersymmetric domain wall.