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Quantum Groups and Integralities in Chern-Simons Theory


Chun, Sungbong (2019) Quantum Groups and Integralities in Chern-Simons Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2CW7-5J29.


In this dissertation, we investigate integralities in Chern-Simons theory. The integralities of interest arise from non-local observables (Wilson lines) in Chern-Simons theory and the partition function itself. In the associated supersymmetric gauge theories (via 3d-3d correspondence), they encode certain BPS spectrum, which are often identified with homological invariants of links and three-manifolds. In this dissertation, we observe that all of them are equipped with non-trivial algebraic structures, such as quantum group actions, modularity, and logarithmic vertex algebras. In the first half of this dissertation, we identify quantum group representations with the dynamics of line operators and their lift to surface operators. In the second half, Chern-Simons partition functions on Seifert manifolds are studied in detail, and its ``hidden'' integralities are identified with quantum modular forms and the characters of logarithmic vertex operator algebra. From the latter, we also observe that quantum group actions control the ``dynamics'' of characters.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Quantum group; Chern-Simons theory; Categorification; Homological Invariants; 3d/3d correspondence; Modular Forms; Log VOA.
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Gukov, Sergei
Thesis Committee:
  • Wise, Mark B. (chair)
  • Ooguri, Hirosi
  • Gukov, Sergei
  • Ni, Yi
Defense Date:3 June 2019
Non-Caltech Author Email:winnety99 (AT)
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Samsung ScholarshipUNSPECIFIED
Record Number:CaltechTHESIS:06072019-210423914
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapter 1 Adapted for Chapter 2
Chun, Sungbong0000-0003-3594-2690
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11723
Deposited By: Sung Bong Chun
Deposited On:10 Jun 2019 23:04
Last Modified:05 Jul 2022 19:09

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