Eleven-dimensional supergravity as a Calabi-Yau twofold
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909412403183616 |
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| author | Hahner, Fabian Saberi, Ingmar |
| author_facet | Hahner, Fabian Saberi, Ingmar |
| contents | We construct a generalization of Poisson-Chern-Simons theory, defined on any supermanifold equipped with an appropriate filtration of the tangent bundle. Our construction recovers interacting eleven-dimensional supergravity in Cederwall's formulation, as well as all possible twists of the theory, and does so in a uniform and geometric fashion. Among other things, this proves that Costello's description of the maximal twist is the twist of eleven-dimensional supergravity in its pure spinor description. It also provides a pure spinor lift of the interactions in the minimally twisted theory. Our techniques enhance the BV formulation of the interactions of each theory to a homotopy Poisson structure by defining a compatible graded-commutative product; this suggests interpretations in terms of deformations of geometric structures on superspace, and provides some concrete evidence for a first-quantized origin of the theories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_12371 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Eleven-dimensional supergravity as a Calabi-Yau twofold Hahner, Fabian Saberi, Ingmar Mathematical Physics High Energy Physics - Theory Quantum Algebra 17B63, 53D17, 17B55, 17B81, We construct a generalization of Poisson-Chern-Simons theory, defined on any supermanifold equipped with an appropriate filtration of the tangent bundle. Our construction recovers interacting eleven-dimensional supergravity in Cederwall's formulation, as well as all possible twists of the theory, and does so in a uniform and geometric fashion. Among other things, this proves that Costello's description of the maximal twist is the twist of eleven-dimensional supergravity in its pure spinor description. It also provides a pure spinor lift of the interactions in the minimally twisted theory. Our techniques enhance the BV formulation of the interactions of each theory to a homotopy Poisson structure by defining a compatible graded-commutative product; this suggests interpretations in terms of deformations of geometric structures on superspace, and provides some concrete evidence for a first-quantized origin of the theories. |
| title | Eleven-dimensional supergravity as a Calabi-Yau twofold |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Algebra 17B63, 53D17, 17B55, 17B81, |
| url | https://arxiv.org/abs/2304.12371 |