期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 339, 期 2, 页码 619-662出版社
SPRINGER
DOI: 10.1007/s00220-015-2401-1
关键词
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资金
- Simons Center for Geometry and Physics, Stony Brook University
- Mathematisches Forschunginstitut Oberwolfach
- DOE [DE-SC0009988]
- ERC Starting Grant - European Research Council under the European Union's Seventh Framework Programme [335739]
We use the 3d-3d correspondence together with the DGG construction of theories T (n) [M] labelled by 3-manifolds M to define a non-perturbative state-integral model for Chern-Simons theory at any level k, based on ideal triangulations. The resulting partition functions generalize a widely studied k = 1 state-integral, as well as the 3d index, which is k = 0. The Chern-Simons partition functions correspond to partition functions of T (n) [M] on squashed lens spaces L(k, 1). At any k, they admit a holomorphic-antiholomorphic factorization, corresponding to the decomposition of L(k, 1) into two solid tori, and the associated holomorphic block decomposition of the partition functions of T (n) [M]. A generalization to L(k, p) is also presented. Convergence of the state integrals, for any k, requires triangulations to admit a positive angle structure; we propose that this is also necessary for the DGG gauge theory T (n) [M] to flow to a desired IR SCFT.
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