Towards Wedge Construction of Four-Dimensional Non-Supersymmetric Theories and Torsion Classes

TL;DR

This paper explores M-theory compactifications on G_2-structured manifolds with torsion, linking non-supersymmetric theories to geometric structures and dualities in string theory.

Contribution

It introduces a novel geometric framework using G_2 torsion classes to characterize supersymmetry breaking and dualities in non-supersymmetric string compactifications.

Findings

G_2 torsion classes effectively describe supersymmetry breaking.

Pinched K3 fibrations relate to SU(3) torsion classes in Type 0 theories.

Potential U-duality between resulting theories in supersymmetric limit.

Abstract

Motivated by recent proposals relating non-supersymmetric Type 0A theory to M-theory compactified on a singular wedge geometry, we study an M-theory compactification on a seven-manifold with G_2 structure, realized as a deformed K3 fibration over a compact three-manifold. In the Morrison--Vafa limit, the deformed K3 may be described locally as a non-trivial torus fibration over a base that is itself a pinched circle fibered over an interval. Once the doubled-spectrum decomposition and the local pinched structure are specified, we show that the G_2 torsion classes provide a natural and efficient way to characterize both the torsion of the seven-manifold and the resulting supersymmetry breaking in four dimensions. Reducing the system to ten dimensions in two inequivalent ways leads respectively to Type 0A and Type 0 heterotic theories compactified on two different non-Kahler manifolds, for which the SU(3) torsion classes furnish the appropriate mathematical description. In particular, we argue that the pinching deformation lies in the 27 of G_2, and that under the two reductions it is distributed differently into the W_2 and W_3 torsion classes of the corresponding SU(3) structures. In the supersymmetric limit, and under suitable assumptions, the two resulting theories may become U-dual to one another. Away from that limit, however, we argue that any such duality should be treated with considerable caution.