TY - JOUR

T1 - Generalising G2 geometry: involutivity, moment maps and moduli

AU - Ashmore, Anthony

AU - Strickland-Constable, Charles

AU - Tennyson, David

AU - Waldram, Daniel

N1 - © 2021 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0 - https://creativecommons.org/licenses/by/4.0/), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

PY - 2021/1/26

Y1 - 2021/1/26

N2 - We analyse the geometry of generic Minkowski N = 1, D = 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds. In type II theories, they extend the notion of Calabi-Yau geometry and include the class of flux backgrounds based on generalised complex structures first considered by Graña et al. (GMPT). Using E
7(7) × ℝ
+ generalised geometry we show that these compactifications are characterised by an SU(7) ⊂ E
7(7) structure defining an involutive subbundle of the generalised tangent space, and with a vanishing moment map, corresponding to the action of the diffeomorphism and gauge symmetries of the theory. The Kähler potential on the space of structures defines a natural extension of Hitchin’s G
2 functional. Using this framework we are able to count, for the first time, the massless scalar moduli of GMPT solutions in terms of generalised geometry cohomology groups. It also provides an intriguing new perspective on the existence of G
2 manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.

AB - We analyse the geometry of generic Minkowski N = 1, D = 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds. In type II theories, they extend the notion of Calabi-Yau geometry and include the class of flux backgrounds based on generalised complex structures first considered by Graña et al. (GMPT). Using E
7(7) × ℝ
+ generalised geometry we show that these compactifications are characterised by an SU(7) ⊂ E
7(7) structure defining an involutive subbundle of the generalised tangent space, and with a vanishing moment map, corresponding to the action of the diffeomorphism and gauge symmetries of the theory. The Kähler potential on the space of structures defines a natural extension of Hitchin’s G
2 functional. Using this framework we are able to count, for the first time, the massless scalar moduli of GMPT solutions in terms of generalised geometry cohomology groups. It also provides an intriguing new perspective on the existence of G
2 manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.

KW - hep-th

KW - math.DG

KW - Flux compactifications

KW - Differential and Algebraic Geometry

UR - http://www.scopus.com/inward/record.url?scp=85100235424&partnerID=8YFLogxK

U2 - 10.1007/JHEP01(2021)158

DO - 10.1007/JHEP01(2021)158

M3 - Article

VL - 2021

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

M1 - 158

ER -