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BPS invariants for Seifert manifolds

Hee-Joong Chung
(Tsinghua University)
Seminar
Wednesday, 1 May, 2019, at 13:00-14:00, in Aud. D1 (1531-113)
Abstract:
The Chern-Simons (CS) partition function or the Witten-Reshtikhin-Turaev (WRT) invariant for 3-manifolds provide the 3-dimensional topological invariants. The knot polynomial invariants, which are obtained from the CS partition function or the WRT invariant for knot complement, is expressed as the q-series with integer powers and integer coefficients, which are necessary properties for the categorification. However, for closed 3-manifolds, it has not been obvious that they have such an integrality property. Recently, it was conjectured by Gukov, Pei, Putrov and Vafa that the CS partition function or the WRT invariant for closed 3-manifolds can be expressed in a particular form in terms of q-series with integer powers and integer coefficients, which is called the homological block. In physics, such q-series can be interpreted as BPS invariants of 3d N=2 theories via the 3d-3d correspondence. In this talk, I will discuss the homological blocks for Seifert manifolds with gauge group G=SU(N).
Organised by: QGM
Contact person: Du Pei