3-Manifolds and 3d indices
3-Manifolds and 3d indices
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DOI：
10.4310/atmp.2013.v17.n5.a3
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发表时间：
2013-01-01
影响因子：
1.5
通讯作者：
Gukov, Sergei
中科院分区：
文献类型：
--
作者：
Dimofte, Tudor;Gaiotto, Davide;Gukov, Sergei
我们确定了一个大类R的三维N = 2超共形场论。这类理论包括作者在以前的工作中讨论过的包裹在三维流形M上的M5-膜的有效理论T-M，更一般地包括承认UV描述为阿贝尔陈-西蒙斯物质理论（可能是非微扰的）超势的理论。在数学上，R类可以被看作是布洛赫群的极端量子推广;特别地，R类中理论之间的等价关系是量子场论的“2到3 "移动。“我们继续研究R类理论的超对称指数，揭示其物理和数学性质，包括与线算子代数和4d指数的关系。对于3-流形理论TM，该指数是一个新的拓扑不变量，它等价于M上的非全纯SL（2，C）Chern-Simons理论，具有一个以前未探索过的“积分圈”。"
We identify a large class R of three-dimensional N = 2 superconformal field theories. This class includes the effective theories T-M of M5-branes wrapped on 3-manifolds M, discussed in previous work by the authors, and more generally comprises theories that admit a UV description as abelian Chern-Simons-matter theories with (possibly non-perturbative) superpotential. Mathematically, class R might be viewed as an extreme quantum generalization of the Bloch group; in particular, the equivalence relation among theories in class R is a quantum-field-theoretic "2 to 3 move." We proceed to study the supersymmetric index of theories in class R, uncovering its physical and mathematical properties, including relations to algebras of line operators and to 4d indices. For 3-manifold theories TM, the index is a new topological invariant, which turns out to be equivalent to non-holomorphic SL(2, C) Chern-Simons theory on M with a previously unexplored "integration cycle."