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Topics in Topological and Holomorphic Quantum Field Theory


Vyas, Ketan D. (2010) Topics in Topological and Holomorphic Quantum Field Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/QPRX-0V43.


We investigate topological quantum field theories (TQFTs) in two, three, and four dimensions, as well as holomorphic quantum field theories (HQFTs) in four dimensions. After a brief overview of the two-dimensional (gauged) A and B models and the corresponding the category of branes, we construct analogous three-dimensional (gauged) A and B models and discuss the two-category of boundary conditions. Compactification allows us to identify the category of line operators in the three-dimensional A and B models with the category of branes in the corresponding two-dimensional A and B models. Furthermore, we use compactification to identify the two-category of surface operators in the four-dimensional GL theory at t = 1 and t = i with the two-category of boundary conditions in the corresponding three-dimensional A and B model, respectively.

We construct a four-dimensional HQFT related to N = 1 supersymmetric quantum chromodynamics (SQCD) with gauge group SU(2) and two flavors, as well as a four-dimensional HQFT related to the Seiberg dual chiral model. On closed Kahler surfaces with h(2,0) > 0, we show that the correlation functions of holomorphic SQCD formally compute certain Donaldson invariants. For simply-connected elliptic surfaces (and their blow-ups), we show that the corresponding correlation functions in the holomorphic chiral model explicitly compute these Donaldson invariants.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Topological Quantum Field Theory, TQFT
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kapustin, Anton N.
Group:Caltech Theory
Thesis Committee:
  • Kapustin, Anton N. (chair)
  • Porter, Frank C.
  • Schwarz, John H.
  • Wise, Mark B.
Defense Date:24 May 2010
Record Number:CaltechTHESIS:06012010-010858409
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5894
Deposited By: Ketan Vyas
Deposited On:04 Jun 2010 20:23
Last Modified:08 Nov 2019 18:11

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