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arxiv: 1112.5179 · v1 · pith:FCHQGQWKnew · submitted 2011-12-21 · ✦ hep-th · math.GT· math.QA

3-Manifolds and 3d Indices

Tudor Dimofte , Davide Gaiotto , Sergei Gukov This is my paper
classification ✦ hep-th math.GTmath.QA
keywords theoriesclassindexindicesmanifoldsabelianadmitalgebras
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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 "2-3 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 T_M, 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."

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