dorsal/arxiv
View SchemaA supergeometric interpretation of vertex operator superalgebras
| Authors | Katrina D. Barron |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9603030 |
| URL | https://arxiv.org/abs/q-alg/9603030 |
Abstract
Huang's geometric interpretation of vertex operator algebras is extended to a supergeometric interpretation of vertex operator superalgebras. In particular, the geometry of spheres with punctures and local analytic coordinates in terms of exponentials of derivations is extended to the geometry of superspheres with punctures, a given spin structure, and local superconformal coordinates in terms of exponentials of superderivations. The notion of supergeometric vertex operator superalgebra is introduced, and in addition, the notion of (superalgebraic) vertex operator superalgebra over a Grassmann algebra and with odd formal variables is introduced. The main result is that the category of supergeometric vertex operator superalgebras over a Grassmann algebra with a given spin structure and the category of vertex operator superalgebras over a Grassmann algebra are isomorphic. In addition, the supergeometric symmetry between the two different possible spin structures naturally gives rise to a symmetry in the superalgebraic structure.
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"abstract": "Huang\u0027s geometric interpretation of vertex operator algebras is extended to a\nsupergeometric interpretation of vertex operator superalgebras. In particular,\nthe geometry of spheres with punctures and local analytic coordinates in terms\nof exponentials of derivations is extended to the geometry of superspheres with\npunctures, a given spin structure, and local superconformal coordinates in\nterms of exponentials of superderivations. The notion of supergeometric vertex\noperator superalgebra is introduced, and in addition, the notion of\n(superalgebraic) vertex operator superalgebra over a Grassmann algebra and with\nodd formal variables is introduced. The main result is that the category of\nsupergeometric vertex operator superalgebras over a Grassmann algebra with a\ngiven spin structure and the category of vertex operator superalgebras over a\nGrassmann algebra are isomorphic. In addition, the supergeometric symmetry\nbetween the two different possible spin structures naturally gives rise to a\nsymmetry in the superalgebraic structure.",
"arxiv_id": "q-alg/9603030",
"authors": [
"Katrina D. Barron"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"title": "A supergeometric interpretation of vertex operator superalgebras",
"url": "https://arxiv.org/abs/q-alg/9603030"
},
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