Alexandria Digital Research Library

Aspects of Three-dimensional Chern-Simons Superconformal Field Theories and their M-theory Interpretation

Author:
Romo Jorquera, Mauricio A.
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
ARK:
ark:/48907/f38k775x
ISBN:
9781267649294
Catalog System Number:
990038915850203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Mauricio Romo
Access: This item is restricted to on-campus access only. Please check our FAQs or contact UCSB Library staff if you need additional assistance.