Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
We describe the infinitesimal moduli space of pairs (Y, V) where Y is a manifold with G2 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 s...
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| Format: | Journal article |
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Springer Verlag
2016
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| author | de la Ossa, X Larfors, M Svanes, E |
| author_facet | de la Ossa, X Larfors, M Svanes, E |
| author_sort | de la Ossa, X |
| collection | OXFORD |
| description | We describe the infinitesimal moduli space of pairs (Y, V) where Y is a manifold with G2 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 G2 cohomology developed by Reyes-Carrión and Fernández and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli $H1d∨A(Y,End(V))Hd∨A1(Y,End(V))$ plus the moduli of the G2 structure preserving the instanton condition. The latter piece is contained in $H1d∨θ(Y,TY)Hd∨θ1(Y,TY),$ and is given by the kernel of a map $F∨F∨$ which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the map $F∨F∨$ is given in terms of the curvature of the bundle and maps $H1d∨θ(Y,TY)Hd∨θ1(Y,TY)$ into $H2d∨A(Y,End(V))Hd∨A2(Y,End(V))$, 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$α′ = 0$. |
| first_indexed | 2024-03-07T02:10:38Z |
| format | Journal article |
| id | oxford-uuid:a083fd1d-af59-4afa-89a1-55cc8c7b22fe |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:10:38Z |
| publishDate | 2016 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:a083fd1d-af59-4afa-89a1-55cc8c7b22fe2022-03-27T02:06:05ZInfinitesimal moduli of G2 holonomy manifolds with instanton bundlesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a083fd1d-af59-4afa-89a1-55cc8c7b22feSymplectic Elements at OxfordSpringer Verlag2016de la Ossa, XLarfors, MSvanes, EWe describe the infinitesimal moduli space of pairs (Y, V) where Y is a manifold with G2 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 G2 cohomology developed by Reyes-Carrión and Fernández and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli $H1d∨A(Y,End(V))Hd∨A1(Y,End(V))$ plus the moduli of the G2 structure preserving the instanton condition. The latter piece is contained in $H1d∨θ(Y,TY)Hd∨θ1(Y,TY),$ and is given by the kernel of a map $F∨F∨$ which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the map $F∨F∨$ is given in terms of the curvature of the bundle and maps $H1d∨θ(Y,TY)Hd∨θ1(Y,TY)$ into $H2d∨A(Y,End(V))Hd∨A2(Y,End(V))$, 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$α′ = 0$. |
| spellingShingle | de la Ossa, X Larfors, M Svanes, E Infinitesimal moduli of G2 holonomy manifolds with instanton bundles |
| title | Infinitesimal moduli of G2 holonomy manifolds with instanton bundles |
| title_full | Infinitesimal moduli of G2 holonomy manifolds with instanton bundles |
| title_fullStr | Infinitesimal moduli of G2 holonomy manifolds with instanton bundles |
| title_full_unstemmed | Infinitesimal moduli of G2 holonomy manifolds with instanton bundles |
| title_short | Infinitesimal moduli of G2 holonomy manifolds with instanton bundles |
| title_sort | infinitesimal moduli of g2 holonomy manifolds with instanton bundles |
| work_keys_str_mv | AT delaossax infinitesimalmoduliofg2holonomymanifoldswithinstantonbundles AT larforsm infinitesimalmoduliofg2holonomymanifoldswithinstantonbundles AT svanese infinitesimalmoduliofg2holonomymanifoldswithinstantonbundles |