= 2 theories from cluster algebras
Abstract
We propose a new description of 3d mathcal {N} = 2 theories which do not admit conventional Lagrangians. Given a quiver Q and a mutation sequence m on it, we define a 3d mathcal {N} = 2 theory mathcal {T}[(Q, m)] in such a way that the S^3_b partition function of the theory coincides with the cluster partition function defined from the pair (Q, m). Our formalism includes the case where 3d mathcal {N} = 2 theories arise from the compactification of the 6d (2,0) A_{N1} theory on a large class of 3manifolds M, including complements of arbitrary links in S^3. 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 3manifold is equipped with a canonical ideal triangulation. Our partition function then coincides with that of the holomorphic part of the SL(N) ChernSimons partition function on M.
 Publication:

Progress of Theoretical and Experimental Physics
 Pub Date:
 February 2014
 DOI:
 10.1093/ptep/ptt115
 arXiv:
 arXiv:1301.5902
 Bibcode:
 2014PTEP.2014b3B01T
 Keywords:

 B10;
 B16;
 B34;
 High Energy Physics  Theory;
 Mathematics  Geometric Topology;
 Mathematics  Quantum Algebra
 EPrint:
 43 pages, 29 figures