Complex Chern-Simons theory at level k via the 3d-3d correspondence

2014/09/02 by Dimofte, Tudor · 2 citations
#FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1409.0857

Abstract

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 SL(n,C) 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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