Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory

TL;DR

This paper explores new methods for including supersymmetry breaking sources in IIA string theory compactifications on solvmanifolds, leading to the construction of de Sitter vacua with positive cosmological constant.

Contribution

It introduces a novel approach to incorporate supersymmetry breaking sources via a generalized polyform, enabling the derivation of de Sitter solutions in string compactifications.

Findings

A new method for including supersymmetry breaking sources in compactifications.

Construction of a de Sitter vacuum solution satisfying all equations.

Positive contribution to the cosmological constant from generalized sources.

Abstract

We consider IIA compactifications on solvmanifolds with O6/D6 branes and study the conditions for obtaining de Sitter vacua in ten dimensions. While this is a popular set-up for searching de Sitter vacua, we propose a new method to include supersymmetry breaking sources. For space-time filling branes preserving bulk supersymmetry, the energy density can easily be extremized with respect to all fields, thanks to the replacement of the DBI action by a pullback of a special form given by a pure spinor. For sources breaking bulk supersymmetry, we propose to replace the DBI action by the pullback of a more general polyform, which is no longer pure. This generalization provides corrections to the energy-momentum tensor which give a positive contribution to the cosmological constant. We find a de Sitter solution to all (bulk and world-volume) equations derived from this action. We argue it solves the equations derived from the standard source action. The paper also contains a review of solvmanifolds.