New G2 holonomy metrics, D6 branes with inherent U(1)xU(1) isometry and gamma-deformations

TL;DR

This paper classifies a broad class of G2 holonomy metrics with inherent U(1) x U(1) isometry, explores their supergravity solutions, and introduces gamma-deformations to generate new fluxed backgrounds, advancing understanding of M-theory compactifications.

Contribution

It identifies the most general local form of G2 metrics with U(1) symmetry, relates them to supergravity solutions, and applies gamma-deformations to produce novel flux backgrounds.

Findings

G2 metrics with U(1) x U(1) isometry are classified.

Supergravity solutions without fluxes are constructed from these metrics.

Gamma-deformations generate new fluxed supergravity solutions.

Abstract

It is found the most general local form of the 11-dimensional supergravity backgrounds which, by reduction along one isometry, give rise to IIA supergravity solutions with a RR field and a non trivial dilaton, and for which the condition $F^{(1,1)}=0$ holds. This condition is stronger than the usual condition $F^{ab}J_{ab}=0$, required by supersymmetry. It is shown that these D6 wrapped backgrounds arise from the direct sum of the flat Minkowski metric with certain G2 holonomy metrics admitting an U(1) action, with a local form found by Apostolov and Salamon. Indeed, the strong supersymmetry condition is equivalent to the statement that there is a new isometry on the G2 manifold, which commutes with the old one; therefore these metrics are inherently toric. An example that is asymptotically Calabi-Yau is presented. There are found another G2 metrics which give rise to half-flat SU(3) structures. All this examples possess an U(1)x U(1)x U(1) isometry subgroup. Supergravity solutions without fluxes corresponding to these G2 metrics are constructed. The presence of a $T^3$ subgroup of isometries permits to apply the \gamma-deformation technique in order to generate new supergravity solutions with fluxes.