| Title:
|
Holomorphic Poisson Field Theories (English) |
| Author:
|
Elliott, Chris |
| Author:
|
Williams, Brian R. |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
5 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
282-309 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct a class of quantum field theories depending on the data of a holomorphic Poisson structure on a piece of the underlying spacetime. The main technical tool relies on a characterization of deformations and anomalies of such theories in terms of the Gelfand--Fuchs cohomology of formal Hamitlonian vector fields. In the case that the Poisson structure is non-degenerate such theories are topological in a certain weak sense, which we refer to as “de Rham topological”. While the Lie algebra of translations acts in a homotopically trivial way, we will show that the space of observables of such a theory does not define an $\Bbb E_n$-algebra. Additionally, we will highlight a conjectural relationship to theories of supergravity in four and five dimensions. (English) |
| Keyword:
|
Quantum field theory |
| Keyword:
|
anomalies |
| Keyword:
|
factorization algebras |
| Keyword:
|
$\Bbb E_n$-algebras |
| Keyword:
|
Gelfand–Fuchs cohomology |
| Keyword:
|
Poisson structures |
| Keyword:
|
supergravity |
| MSC:
|
17B65 |
| MSC:
|
18N70 |
| MSC:
|
81T50 |
| idZBL:
|
Zbl 1486.81148 |
| idMR:
|
MR4367223 |
| DOI:
|
10.21136/HS.2021.08 |
| . |
| Date available:
|
2026-03-13T05:37:36Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153440 |
| . |
| Reference:
|
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| Reference:
|
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[24] Williams, Brian R: On the local cohomology of holomorphic vector fields..To appear |
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|
[25] Williams, Brian R.: Renormalization for holomorphic field theories..Comm. Math. Phys., 374(3):1693–1742 MR 4076086 |
| . |
