Twisted eleven-dimensional supergravity

Raghavendran, Surya; Saberi, Ingmar; Williams, Brian R.

doi:10.48550/arxiv.2111.03049

“…Their work derives the holomorphic twist of the eleven-dimensional three-form multiplet. Starting from the holomorphic twist of Saberi-Williams, Ingmar Saberi, Surya Raghavendran and Brian Williams independently derive the G 2 × SU (2) invariant twist in their forthcoming work [31]. Our work is complementary to that of Saberi-Williams and Raghavendran-Saberi-Williams in the sense that we determine the origin of the twisted fields in the untwisted theory, whereas their work cleverly bypasses the component fields of the untwisted theory.…”

Section: Note Addedmentioning

confidence: 89%

Maximally Twisted Eleven-Dimensional Supergravity

Eager¹,

Hahner

²

2022

Commun. Math. Phys.

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We perform the maximal twist of eleven-dimensional supergravity. This twist is partially topological and exists on manifolds of $$G_2 \times SU(2)$$ G 2 × S U ( 2 ) holonomy. Our derivation starts with an explicit description of the Batalin–Vilkovisky complex associated to the three-form multiplet in the pure spinor superfield formalism. We then determine the $$L_\infty $$ L ∞ module structure of the supersymmetry algebra on the component fields. We twist the theory by modifying the differential of the Batalin–Vilkovisky complex to incorporate the action of a scalar supercharge. We find that the resulting free twisted theory is given by the tensor product of the de Rham and Dolbeault complexes of the respective $$G_2$$ G 2 and SU(2) holonomy manifolds as conjectured by Costello.

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“…It would be interesting to understand the action functionals of [8,10] in this language, and to use them to connect to component actions for perturbative supergravity, either twisted or untwisted. An interacting BV theory conjecturally describing the minimal twist of eleven-dimensional supergravity was studied in [51].…”

Section: Further Directionsmentioning

confidence: 99%

The Derived Pure Spinor Formalism as an Equivalence of Categories

Elliott¹,

Hahner²,

Saberi³

2023

SIGMA

0

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We construct a derived generalization of the pure spinor superfield formalism and prove that it exhibits an equivalence of dg-categories between multiplets for a supertranslation algebra and equivariant modules over its Chevalley-Eilenberg cochains. This equivalence is closely linked to Koszul duality for the supertranslation algebra. After introducing and describing the category of supermultiplets, we define the derived pure spinor construction explicitly as a dg-functor. We then show that the functor that takes the derived supertranslation invariants of any supermultiplet is a quasi-inverse to the pure spinor construction, using an explicit calculation. Finally, we illustrate our findings with examples and use insights from the derived formalism to answer some questions regarding the ordinary (underived) pure spinor superfield formalism.

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“…It would be interesting to understand the action functionals of [Ced10c;Ced10a] in this language, and to use them to connect to component actions for perturbative supergravity, either twisted or untwisted. An interacting BV theory conjecturally describing the minimal twist of eleven-dimensional supergravity was studied in [RSW21].…”

Section: Bnmentioning

confidence: 99%

The derived pure spinor formalism as an equivalence of categories

Elliott¹,

Hahner²,

Saberi³

2022

Preprint

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We construct a derived generalization of the pure spinor superfield formalism and prove that it exhibits an equivalence of dg-categories between multiplets for a supertranslation algebra and equivariant modules over its Chevalley-Eilenberg cochains. This equivalence is closely linked to Koszul duality for the supertranslation algebra. After introducing and describing the category of supermultiplets, we define the derived pure spinor construction explicitly as a dg-functor. We then show that the functor that takes the derived supertranslation invariants of any supermultiplet is a quasi-inverse to the pure spinor construction, using an explicit calculation. Finally, we illustrate our findings with examples and use insights from the derived formalism to answer some questions regarding the ordinary (underived) pure spinor superfield formalism.

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Twisted eleven-dimensional supergravity

Cited by 3 publications

References 31 publications

Maximally Twisted Eleven-Dimensional Supergravity

Maximally Twisted Eleven-Dimensional Supergravity

The Derived Pure Spinor Formalism as an Equivalence of Categories

The derived pure spinor formalism as an equivalence of categories

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