Duality, Quantum Vortices and Anyons in Maxwell-Chern-Simons-Higgs Theories

Abstract

The order-disorder duality structure is exploited in order to obtain a quantum description of anyons and vortices in: a) the Maxwell theory; b) the Abelian Higgs Model; c) the Maxwell-Chern-Simons theory; d) the Maxwell-Chern-Simons-Higgs theory. A careful construction of a charge bearing order operator($\sigma$) and a magnetic flux bearing disorder operator (vortex operator) ($\mu$) is performed, paying attention to the necessary requirements for locality. An anyon operator is obtained as the product $\phi =\sigma \mu$. A detailed and comprehensive study of the euclidean correlation functions of $\sigma$, $\mu$ and $\phi$ is carried on in the four theories above. The exact correlation functions are obtained in cases $\underline{a}$ and $\underline{c}$. The large distance behavior of them is obtained in cases $\underline{b}$ and $\underline{d}$. The study of these correlation functions allows one to draw conclusions about the condensation of charge and magnetic flux, establishing thereby an analogy with the Ising model. The mass of vortex and anyon excitations is explicitly obtained wherever these excitations are present in the spectrum. The independence between the mechanisms of mass generation for the vortices and for the vector field is clearly exposed.

58 pages; 6 figures (available from the author upon request); Latex; Princeton report PUPT-1330

Cited by in corpus (10)

• Particle-vortex duality in topological insulators and superconductors
• Quantum Theory of Strings in Abelian Higgs Model
• Dual description of the superconducting phase transition
• Cancellation of quantum anomalies and bosonization of three-dimensional time-reversal symmetric topological insulators
• Class of self-dual models in three dimensions
• Deriving three-dimensional bosonization and the duality web
• Particle-vortex duality and theta terms in AdS/CMT applications
• Charge and Magnetic Flux Correlations in Chern-Simons Theory with Fermions
• Creation operators for 2-branes and duality in BF and Chern-Simons theories in D=5
• Local Quantum Fields for Anyons on the Circle leading to Non-Relativistic Anyons in Two Dimensions