Semiclassical Analysis of the 3d/3d Relation

Abstract

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 Teichmuller theory. We also show that the subleading correction to the partition function reproduces the Reidemeister torsion.

23 pages, 4 figures; v2: typos corrected, published in PRD

References in corpus (8)

• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• 3d Partition Function as Overlap of Wavefunctions
• AGT on the S-duality Wall
• On 3d extensions of AGT relation
• The Volume Conjecture and Topological Strings

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