Vanishing Cosmological Constant by Gravitino-Dressed Compactification of 11D Supergravity

TL;DR

This paper explores a novel compactification mechanism in eleven-dimensional supergravity where gravitino fields induce solutions with vanishing cosmological constant, leading to flat external spacetime, by utilizing torsion without affecting the Riemann tensor.

Contribution

It introduces gravitino-induced compactifications that produce flat external spacetime without a cosmological constant, expanding understanding of supergravity solutions beyond supersymmetric cases.

Findings

Constructed solutions with gravitino and three-form fields leading to flat spacetime.

Demonstrated internal space can be parallelized without generating a cosmological constant.

Showed torsion replaces the cosmological constant in these compactifications.

Abstract

We consider compactifications induced by the gravitino field of eleven dimensional supergravity. Such compactifications are not trivial in the sense that the gravitino profiles are not related to pure bosonic ones by means of a supersymmetry transformation. The basic property of such backgrounds is that they admit $\psi$-torsion although they have vanishing Riemann tensor. Thus, these backgrounds may be considered also as solutions of the teleparallel formulation of supergravity. We construct two classes of solutions, one with both antisymmetric three-form field, gravity and gravitino and one with only gravity and gravitino. In these classes of solutions, the internal space is a parallelized compact manifold, so that it does not inherit any cosmological constant to the external spacetime. The latter turns out to be flat Minkowski in the maximally symmetric case. The elimination of the cosmological constant in the spontaneously compactified supergravity seems to be a generic property based on the trading of the cosmological constant for parallelizing torsion.