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NHETC Seminar - q-nonabelianization for line defects

Date and Time: Tuesday, February 04, 2020, 03:00pm - 04:00pm
Location: 385E

NHETC Seminar

Fei Yan (Rutgers)

q-nonabelianization for line defects

Abstract: I will talk about joint work with Andrew Neitzke on the q-nonabelianization map, which maps links L in a 3-manifold M to links L' in a branched N-fold cover M'. From the quantum field theory point of view, q-nonabelianization is an UV-IR map relating two different kinds of defects. In the UV, we consider the 6d (2,0) superconformal field theory of type gl(N) on M × R2,1, with surface defects inserted along L×Rt where Rt is the time direction. In the IR, we have the 6d (2,0) theory of type gl(1) on M' × R2,1 with surface defects inserted along L'×Rt . In two special cases, the q-nonabelianization map computes familiar objects. When M=R^3, the map gives Jones polynomial of the link L; when M=C×R and the projection of L on C doesn't contain crossings, the map computes the protected spin character for framed BPS states in 4d theories of class-S. I'll give a concrete construction of the q-nonabelianization map for N=2 and M=C×R, using WKB foliation data associated with a holomorphic covering C'--->C.

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