2013/01/24 by Yuji Terashima, Masahito Yamazaki · 1 voice
Mathematics · Physics and Astronomy · #hep-th #math.GT #math.QA
paper · pdf · doi:10.1093/ptep/ptt115
published as Prog.Theor.Exp.Phys.023:B01,2014 · 43 pages, 29 figures; v2: restructured and typos corrected
arxiv published 2013/01/24 · arxiv created 2014/01/27 · arxiv updated 2014/01/27
We propose a new description of 3d N=2 theories which do not admit conventional Lagrangians. Given a quiver Q and a mutation sequence m on it, we define a 3d N=2 theory T[(Q,m)] in such a way that the S3b partition function of the theory coincides with the cluster partition function defined from the pair (Q, m). Our formalism includes the case where 3d N=2 theories arise from the compactification of the 6d (2,0) AN-1 theory on a large class of 3-manifolds M, including complements of arbitrary links in S3. In this case the quiver is defined from a 2d ideal triangulation, the mutation sequence represents an element of the mapping class group, and the 3-manifold is equipped with a canonical ideal triangulation. Our partition function then coincides with that of the holomorphic part of the SL(N) Chern-Simons partition function on M.