Tunneling, the Quillen metric and analytic torsion for high powers of a holomorphic line bundle
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arXiv
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| Formato: | Preprint |
| Publicado: |
2011
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| _version_ | 1866918021686099968 |
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| author | Berman, Robert J. |
| author_facet | Berman, Robert J. |
| contents | Let L be a line bundle over a compact complex manifold X and endow L and TX with Hermitian metrics. Our main result provides a formula for the average distribution of the exponentially small eigenvalues of the corresponding Dolbeault Laplacians associated to high tensor powers of L; which in physics terminology is a measure of "tunneling" of the Dolbeault complex. Along the way a new proof of the asymptotics of the induced Quillen metric on the corresponding determinant line is obtained. A brief comparison with the tunneling effect for Witten Laplacians and large deviation principles for fermions is also made. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1106_2965 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Tunneling, the Quillen metric and analytic torsion for high powers of a holomorphic line bundle Berman, Robert J. Differential Geometry Mathematical Physics Algebraic Geometry Let L be a line bundle over a compact complex manifold X and endow L and TX with Hermitian metrics. Our main result provides a formula for the average distribution of the exponentially small eigenvalues of the corresponding Dolbeault Laplacians associated to high tensor powers of L; which in physics terminology is a measure of "tunneling" of the Dolbeault complex. Along the way a new proof of the asymptotics of the induced Quillen metric on the corresponding determinant line is obtained. A brief comparison with the tunneling effect for Witten Laplacians and large deviation principles for fermions is also made. |
| title | Tunneling, the Quillen metric and analytic torsion for high powers of a holomorphic line bundle |
| topic | Differential Geometry Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/1106.2965 |