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Topics in topological and holomorphic quantum field theory


Vyas, Ketan (2010) Topics in topological and holomorphic quantum field theory. Dissertation (Ph.D.), California Institute of Technology.


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 K ̈ahler 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.
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:26 Dec 2012 03:27

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