Generalising G2 geometry: involutivity, moment maps and moduli
Abstract
We analyse the geometry of generic Minkowski = 1, = 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 E7(7)× $$\mathbb{R}$$+generalised geometry we show that these compactifications are characterised by an SU(7) ⊂ E7(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 G2functional. 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 G2manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.
- Authors:
-
- Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics & Astronomy
- Univ. of Hertfordshire, Hatfield (United Kingdom). School of Physics, Astronomy and Mathematics
- Imperial College, London (United Kingdom). Dept. of Physics
- Publication Date:
- Research Org.:
- Univ. of Pennsylvania, Philadelphia, PA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); Science and Technology Facilities Council (STFC)
- OSTI Identifier:
- 1851030
- Grant/Contract Number:
- SC0007901; ST/P000762/1
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2021; Journal Issue: 1; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Differential and Algebraic Geometry; Flux compactifications
Citation Formats
Ashmore, Anthony, Strickland-Constable, Charles, Tennyson, David, and Waldram, Daniel. Generalising G2 geometry: involutivity, moment maps and moduli. United States: N. p., 2021.
Web. doi:10.1007/jhep01(2021)158.
Ashmore, Anthony, Strickland-Constable, Charles, Tennyson, David, & Waldram, Daniel. Generalising G2 geometry: involutivity, moment maps and moduli. United States. https://doi.org/10.1007/jhep01(2021)158
Ashmore, Anthony, Strickland-Constable, Charles, Tennyson, David, and Waldram, Daniel. Tue .
"Generalising G2 geometry: involutivity, moment maps and moduli". United States. https://doi.org/10.1007/jhep01(2021)158. https://www.osti.gov/servlets/purl/1851030.
@article{osti_1851030,
title = {Generalising G2 geometry: involutivity, moment maps and moduli},
author = {Ashmore, Anthony and Strickland-Constable, Charles and Tennyson, David and Waldram, Daniel},
abstractNote = {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 E7(7)× $\mathbb{R}$+generalised geometry we show that these compactifications are characterised by an SU(7) ⊂ E7(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 G2functional. 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 G2manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.},
doi = {10.1007/jhep01(2021)158},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2021,
place = {United States},
year = {Tue Jan 26 00:00:00 EST 2021},
month = {Tue Jan 26 00:00:00 EST 2021}
}
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