TY - JOUR

T1 - N = 2 theories from cluster algebras

AU - Terashima, Yuji

AU - Yamazaki, Masahito

PY - 2014/2

Y1 - 2014/2

N2 - 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 theoryT [(Q,m)] in such a way that the S3 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 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 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.

AB - 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 theoryT [(Q,m)] in such a way that the S3 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 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 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.

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U2 - 10.1093/ptep/ptt115

DO - 10.1093/ptep/ptt115

M3 - Article

AN - SCOPUS:84898425833

SN - 2050-3911

VL - 2014

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

IS - 2

M1 - 023B01

ER -