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Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
Univ Oxford, Math Inst, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England..
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
UPMC Univ Paris 06, Sorbonne Univ, UMR 7589, LPTHE, F-75005 Paris, France.;CNRS, UMR 7589, LPTHE, F-75005 Paris, France.;Sorbonne Univ, Inst Lagrange Paris, 98 Bis Bd Arago, F-75014 Paris, France..
2016 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 11, article id 016Article in journal (Refereed) Published
Abstract [en]

We describe the infinitesimal moduli space of pairs (Y, V) where Y is a manifold with G(2) holonomy, and V is a vector bundle on Y with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical G(2) cohomology developed by Reyes-Carrion and Fern\'andez and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli H-d(sic)A(1)(Y, End(V)) plus the moduli of the G(2) structure preserving the instanton condition. The latter piece is contained in H-d(sic)theta(1)(Y, TY), and is given by the kernel of a map F(sic) which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the map F(sic) is given in terms of the curvature of the bundle and maps H-d(sic)theta(1)(Y, TY) into H-d(sic)A(2) (Y, End(V)), and moreover can be used to define a cohomology on an extension bundle of TY by End(V). We comment further on the resemblance with the holomorphic Atiyah algebroid and connect the story to physics, in particular to heterotic compactifications on (Y,V) when alpha'=0.

Place, publisher, year, edition, pages
SPRINGER , 2016. no 11, article id 016
Keywords [en]
Superstrings and Heterotic Strings, Differential and Algebraic Geometry, Superstring Vacua
National Category
Subatomic Physics
Identifiers
URN: urn:nbn:se:uu:diva-322003DOI: 10.1007/JHEP11(2016)016ISI: 000399293300001OAI: oai:DiVA.org:uu-322003DiVA, id: diva2:1095580
Available from: 2017-05-15 Created: 2017-05-15 Last updated: 2017-05-15Bibliographically approved

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Larfors, Magdalena
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