Abstract
We use the 3d3d correspondence together with the DGG construction of theories Tn[M] labelled by 3manifolds M to define a nonperturbative stateintegral model for SL(n,C) ChernSimons theory at any level k, based on ideal triangulations. The resulting partition functions generalize a widely studied k=1 stateintegral as well as the 3d index, which is k=0. The ChernSimons partition functions correspond to partition functions of Tn[M] on squashed lens spaces L(k,1). At any k, they admit a holomorphicantiholomorphic 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.
Original language  English 

Pages (fromto)  619–662 
Number of pages  49 
Journal  Communications in Mathematical Physics 
Volume  339 
Issue number  2 
Early online date  16 Jun 2015 
DOIs  
Publication status  Published  31 Oct 2015 
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Tudor Dimofte
 School of Mathematics  Reader in Algebra, Geometry & Topology and related fields
Person: Academic: Research Active (Teaching)