dorsal/arxiv
View SchemaAlmost Parity Structure, Connections and Vielbeins in BV Geometry
| Authors | K. Bering |
|---|---|
| Categories | |
| ArXiv ID | physics/9711010 |
| URL | https://arxiv.org/abs/physics/9711010 |
Abstract
We observe that an anti-symplectic manifold locally always admits a parity structure. The parity structure can be viewed as a complex-like structure on the manifold. This induces an odd metric and its Levi-Civita connection, and thereby a new notion of an odd Kaehler geometry. Oversimplified, just to capture the idea, the bosonic variables are ``holomorphic'', while the fermionic variables are ``anti-holomorphic''. We find that an odd Kaehler manifold in this new ``complex'' sense has a nilpotent odd Laplacian iff it is Ricci-form-flat. The local cohomology of the odd Laplacian is derived. An odd Calabi-Yau manifold has locally a canonical volume form. We suggest that an odd Calabi-Yau manifold is the natural geometric notion to appear in covariant BV-quantization. Finally, we give a vielbein formulation of anti-symplectic manifolds.
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"abstract": "We observe that an anti-symplectic manifold locally always admits a parity\nstructure. The parity structure can be viewed as a complex-like structure on\nthe manifold. This induces an odd metric and its Levi-Civita connection, and\nthereby a new notion of an odd Kaehler geometry. Oversimplified, just to\ncapture the idea, the bosonic variables are ``holomorphic\u0027\u0027, while the\nfermionic variables are ``anti-holomorphic\u0027\u0027. We find that an odd Kaehler\nmanifold in this new ``complex\u0027\u0027 sense has a nilpotent odd Laplacian iff it is\nRicci-form-flat. The local cohomology of the odd Laplacian is derived. An odd\nCalabi-Yau manifold has locally a canonical volume form. We suggest that an odd\nCalabi-Yau manifold is the natural geometric notion to appear in covariant\nBV-quantization. Finally, we give a vielbein formulation of anti-symplectic\nmanifolds.",
"arxiv_id": "physics/9711010",
"authors": [
"K. Bering"
],
"categories": [
"math-ph",
"hep-th",
"math.DG",
"math.MP"
],
"title": "Almost Parity Structure, Connections and Vielbeins in BV Geometry",
"url": "https://arxiv.org/abs/physics/9711010"
},
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