Towards non-perturbative BV-theory via derived differential geometry
| Autor: | Alfonsi, Luigi, Young, Charles A. S. |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We propose a global geometric framework which allows one to encode a natural non-perturbative generalisation of usual Batalin-Vilkovisky (BV-)theory. Namely, we construct a concrete model of derived differential geometry, whose geometric objects are formal derived smooth stacks, i.e. stacks on formal derived smooth manifolds, together with a notion of differential geometry on them. This provides a working language to study generalised geometric spaces that are smooth, infinite-dimensional, higher and derived at the same time. Such a formalism is obtained by combining Schreiber's differential cohesion with the machinery of T\"oen-Vezzosi's homotopical algebraic geometry applied to the theory of derived manifolds of Spivak and Carchedi-Steffens. We investigate two classes of examples of non-perturbative classical BV-theories in the context of derived differential cohesion: scalar field theory and Yang-Mills theory. Comment: 106 pages, 11 figures; section 4 revised, other corrections |
| Databáze: | arXiv |
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