M-Theory Vacua from Warped Compactifications on Spin(7) Manifolds

TL;DR

This paper explores how higher-order quantum corrections deform M-theory compactifications on Spin(7) manifolds, leading to warped solutions with fluxes and breaking Ricci flatness while preserving supersymmetry.

Contribution

It derives perturbative solutions for warped M-theory compactifications on Spin(7) manifolds with fluxes, identifying conditions for supersymmetric vacua beyond leading order.

Findings

Ricci flatness is generally lost due to quantum corrections.

Supersymmetric vacua are identified within warped compactifications.

Evaluation of quartic polynomial J0 on Spin(7) manifolds is performed.

Abstract

At the leading order, M-theory admits minimal supersymmetric compactifications if the internal manifold has exceptional holonomy. Once we take into account higher order quantum correction terms in the low energy effective action, the supergravity vacua have to be deformed away from the exceptional holonomy if we want to preserve the supersymmetry of the solution. In this paper we discuss the Spin(7) holonomy case. We derive a perturbative set of solutions which emerges from a warped compactification with non-vanishing flux for the M-theory field strength and we identify the supersymmetric vacua out of this general set of solutions. For this purpose we have to evaluate the value of the quartic polynomial J0 on a Spin(7) holonomy manifold as well as its first variation with respect to the internal metric. We show that in general the Ricci flatness of the internal manifold is lost.