Local superconformal algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929537575550976 |
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| author | Hahner, Fabian Raghavendran, Surya Saberi, Ingmar Williams, Brian R. |
| author_facet | Hahner, Fabian Raghavendran, Surya Saberi, Ingmar Williams, Brian R. |
| contents | Given a supermanifold equipped with an odd distribution of maximal dimension and constant symbol, we construct the formal moduli problem of deformations of the distribution. This moduli problem is described by a local super dg Lie algebra that provides both a resolution of the structure-preserving vector fields on superspace and a derived enhancement of superconformal symmetry. Applying our construction in standard physical examples returns the conformal supergravity multiplet in every known example, in any dimension and with any amount of supersymmetry$\unicode{x2014}$whether or not a superconformal algebra exists. We discuss new examples related to twisted supergravity, higher Virasoro algebras, and exceptional super Lie algebras. The compatibility of our techniques with twisting also leads to a computation of every twist of the stress tensor multiplet of a superconformal theory, including universal operator product expansions. Our approach uses a derived model for the space of functions constant along the distribution, which is applicable even when the distribution is non-involutive; we construct other natural multiplets, such as Kähler differentials, that appear naturally through this lens on superspace geometry. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_08176 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local superconformal algebras Hahner, Fabian Raghavendran, Surya Saberi, Ingmar Williams, Brian R. Mathematical Physics High Energy Physics - Theory Differential Geometry 17B55, 83E50, 17B81, 53C15 Given a supermanifold equipped with an odd distribution of maximal dimension and constant symbol, we construct the formal moduli problem of deformations of the distribution. This moduli problem is described by a local super dg Lie algebra that provides both a resolution of the structure-preserving vector fields on superspace and a derived enhancement of superconformal symmetry. Applying our construction in standard physical examples returns the conformal supergravity multiplet in every known example, in any dimension and with any amount of supersymmetry$\unicode{x2014}$whether or not a superconformal algebra exists. We discuss new examples related to twisted supergravity, higher Virasoro algebras, and exceptional super Lie algebras. The compatibility of our techniques with twisting also leads to a computation of every twist of the stress tensor multiplet of a superconformal theory, including universal operator product expansions. Our approach uses a derived model for the space of functions constant along the distribution, which is applicable even when the distribution is non-involutive; we construct other natural multiplets, such as Kähler differentials, that appear naturally through this lens on superspace geometry. |
| title | Local superconformal algebras |
| topic | Mathematical Physics High Energy Physics - Theory Differential Geometry 17B55, 83E50, 17B81, 53C15 |
| url | https://arxiv.org/abs/2410.08176 |