Seminar on QFT and Geometry | Non-hyperbolic 3-manifolds and bulk dual 3D field theories of 2D Virasoro minimal models

Abstract：

Using 3D-3D correspondence, we construct 3D dual bulk field theories of general Virasoro minimal models $M(P,Q)$. They correspond to Seifert fiber spaces $S^2 ((P,R-P),(Q,-S),(3,1))$ with two integers $(R,S)$ satisfying $PS-QR =1$. For unitary case, i.e. $|P-Q|=1$, the bulk theory has a mass gap and flows to an unitary topological field theory (TQFT) in the IR which is expected to support the chiral Virasoro minimal model at the boundary upon a proper boundary condition. For non-unitary case, i.e. $|P-Q|>1$, the bulk theory flows to a 3D $\CN=4$ rank-0 superconformal field theory, whose topologically twisted theory supports the chiral minimal model at the boundary. We also give concrete field theory description of the 3D bulk theory using $T[SU(2)]$ theories.