Three-Dimensional Superconformal Field Theory, Chern-Simons Theorv, and Their Correspondence

Author: Chung, Hee Joong

Year: 2014

Degree: Dissertation (Ph.D.)

Advisors: Gukov, Sergei; Schwarz, John H.

Committee Members: Gukov, Sergei; Schwarz, John H.; Kapustin, Anton N.; Porter, Frank C.

Option: Physics

DOI: 10.7907/7CA7-9C79

Abstract

In this thesis, we discuss 3d-3d correspondence between Chern-Simons theory and three-dimensional N = 2 superconformal field theory. In the 3d-3d correspondence proposed by Dimofte-Gaiotto-Gukov information of abelian flat connection in Chern-Simons theory was not captured. However, considering M-theory configuration giving the 3d-3d correspondence and also other several developments, the abelian flat connection should be taken into account in 3d-3d correspondence. With help of the homological knot invariants, we construct 3d N = 2 theories on knot complement in 3-sphere for several simple knots. Previous theories obtained by Dimofte-Gaiotto-Gukov can be obtained by Higgsing of the full theories. We also discuss the importance of all flat connections in the 3d-3d correspondence by considering boundary conditions in 3d N = 2 theories and 3-manifold.

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