1301.5902 (Yuji Terashima et al.)

3d N=2 Theories from Cluster Algebras    [PDF]

Yuji Terashima, Masahito Yamazaki

We conjecture that a new class of 3d N=2 theories are associated with a quiver Q and a mutation sequence m on it. We define the cluster partition function from the pair (Q, m), and this partition function coincides with the S^3_b partition function of the associated 3d N=2 theory T[(Q,m)]. Our formalism includes the case where 3d N=2 theories arise from the compactification of the 6d (2,0) A_{N-1} theory on a large class of 3-manifolds 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 3-manifold is equipped with a canonical ideal triangulation. Our partition function coincides with that of the holomorphic part of the SL(N) Chern-Simons partition function on M; when N=2 and M is hyperbolic, the partition function reproduces the gluing conditions of ideal hyperbolic tetrahedra in the semiclassical limit.

View original: http://arxiv.org/abs/1301.5902