Aspects of Three-dimensional Chern-Simons Superconformal Field Theories and their M-theory Interpretation
- Degree Grantor:
- University of California, Santa Barbara. Physics
- Degree Supervisor:
- David E. Berenstein
- Place of Publication:
- [Santa Barbara, Calif.]
- Publisher:
- University of California, Santa Barbara
- Creation Date:
- 2012
- Issued Date:
- 2012
- Topics:
- Physics, Theory, Physics, Elementary Particles and High Energy, and Physics, General
- Genres:
- Online resources and Dissertations, Academic
- Dissertation:
- Ph.D.--University of California, Santa Barbara, 2012
- Description:
In this thesis we study different aspects of three-dimensional superconformal Chern-Simons theories that are good candidates to be realized as worldvolume theories of M2-branes. We begin by studying the moduli space of vacua of abelian and non-abelian A-D-E orbifolds of the ABJM model and we find that in the dual M-theory setup, the M-theory fiber is divided by the product of the Chern-Simons level times the order of the orbifold group. We also see a direct relation in this setup between the Chern-Simons levels of the different groups and fluxes for fractional brane cycles. We further generalize this analysis to orbifolds with discrete torsion of the ABJM theory by a finite subgroup Gamma of SU(2) x SU(2). It is shown that, in general, the order m of the cocycle we chose to twist the algebra by, enters in a non-trivial way in the moduli space of vacua of the resulting theory. In order to compute more general moduli spaces a semiclassical method to analyze the spectrum of BPS monopole operators of N = 2 superconformal field theories in 3d is proposed. We show that the chiral ring of the theory results from the semiclassical holomorphic quantization of the solution of classical BPS equations of motion on the cylinder. We apply this formalism to various theories. We also use these techniques to compare the chiral rings of theories that might be related to each other via Seiberg dualities in four dimensions in the classical limit. We find that the change of basis transformations that generate dualities in four dimensions generically do not work in three dimensions in the presence of Chern-Simons terms. We also determine the spectrum of R-charges of the chiral ring operators by assembling them on a Hilbert series and by minimizing the coefficient of the maximum pole relative to the trial R-charge. This is related to volume minimization in theories with dual supergravity setups.
- Physical Description:
- 1 online resource (308 pages)
- Format:
- Text
- Collection(s):
- UCSB electronic theses and dissertations
- Other Versions:
- http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3540261
- ARK:
- ark:/48907/f38k775x
- ISBN:
- 9781267649294
- Catalog System Number:
- 990038915850203776
- Copyright:
- Mauricio Romo, 2012
- Rights:
- In Copyright
- Copyright Holder:
- Mauricio Romo
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