A Caltech Library Service

Symmetries in Three-Dimensional Superconformal Quantum Field Theories


Bashkirov, Denis (2012) Symmetries in Three-Dimensional Superconformal Quantum Field Theories. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/61EK-5K70.


Many examples of gauge-gravity duality and quantum equivalences of different-looking three-dimensional Quantum Field Theories indicate the existence of continuous symmetries whose currents are not built from elementary, or perturbative, elds used to write down the Lagrangian. These symmetries are called hidden or nonperturbative.

We describe a method for studying continuous symmetries in a large class of three-dimensional supersymmetric gauge theories which, in particular, enables one to explore nonperturbative global symmetries and supersymmetries. As an application of the method, we prove conjectured supersymmetry enhancement in strongly coupled ABJM theory from N = 6 to N = 8 and nd additional nonperturbative evidence for its duality to the N = 8 U(N) SYM theory for the minimal value of the Chern-Simons coupling. Hidden supersymmetry is also shown to occur in N = 4 d = 3 SQCD with one fundamental and one adjoint hypermultiplets. An innite family of N = 6 d = 3 ABJ theories is proved to have hidden N = 8 superconformal symmetry and hidden parity on the quantum level. We test several conjectural dualities between ABJ theories and theories proposed by Bagger and Lambert, and Gustavsson by comparing superconformal indices of these theories. Comparison of superconformal indices is also used to test dualities between N = 2 d = 3 theories proposed by Aharony, the analysis of whose chiral rings teaches some general lessons about nonperturbative chiral operators of strongly coupled 3d supersymmetric gauge theories.

As another application of our method we consider examples of hidden global symmetries in a class of quiver three-dimensional N = 4 superconformal gauge theories. Finally, we point out to the relations between some basic properties of superconformal N = 6 theories and their symmetries.

The results presented in this thesis were obtained in a series of papers [1, 2, 3, 4, 5].

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Superconformal Quantum Field Theory, nonperturbative symmetries, Monopole operators.
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)
  • Schwarz, John H.
  • Porter, Frank C.
  • Wise, Mark B.
Defense Date:7 May 2012
Record Number:CaltechTHESIS:05112012-122450178
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7023
Deposited By: Denis Bashkirov
Deposited On:14 May 2012 22:10
Last Modified:03 Oct 2019 23:55

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page