Semiclassical analysis of the 3d/3d relation

Yuji Terashima, Masahito Yamazaki

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


We provide quantitative evidence for our previous conjecture which states an equivalence of the partition function of a 3d N=2 gauge theory on a duality wall and that of the SL(2,R) Chern-Simons theory on a mapping torus, for a class of examples associated with once-punctured torus. In particular, we demonstrate that a limit of the 3d N=2 partition function reproduces the hyperbolic volume and the Chern-Simons invariant of the mapping torus. This is shown by analyzing the classical limit of the trace of an element of the mapping class group in the Hilbert space of the quantum Teichmüller theory. We also show that the subleading correction to the partition function reproduces the Reidemeister torsion.

Original languageEnglish
Article number026011
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number2
Publication statusPublished - 2013 Jul 18


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