The Aharonov-Bohm effect and exotic statistics for non-abelian vortices (original) (raw)

What Becomes of Giant Vortices in the Abelian Higgs Model

Physical Review Letters

We discuss vortex solutions of the Abelian Higgs model in the limit of large winding number n. We suggest a framework where a topological quantum number n is associated with a ratio of dynamical scales and a systematic expansion in inverse powers of n is then derived in the spirit of effective field theory. The general asymptotic form of giant vortices is obtained. For critical coupling the axially symmetric vortices become integrable in the large-n limit and we present the corresponding analytic solution. The method provides simple asymptotic formulas for the vortex shape and parameters with accuracy that can be systematically improved, and can be applied to topological solitons of other models. After including the next-to-leading terms the approximation works remarkably well down to n ¼ 1.

UCTP-120-99 Vortex solutions in nonabelian Higgs theories

2000

A new class of vortex solutions is found in SU(2) gauge theories with two adjoint representation Higgs bosons. Implications of these new solutions and their possible connection with Center Gauge fixed pure gauge theories are discussed. PACS numbers: 11.15Kc, 11.15Ha, 12.38Aw The classification of vortex solutions in SU(N) gauge theories requires the investigation of mapping rotations around the vortex axis (U(1) group) into SU(N). Unfortunately, all such maps are continuously deformable into the trivial map. If one considers the group SU(N)/ZN instead of SU(N) then one finds nontrivial homotopy classes classified by the abelian group, ZN. Then vortex solutions of finite free energy (but infinite energy) could exist in four-dimensional and finite energy solitons could exist in three-dimensional SU(N)/ZN gauge theories. [1] A prime candidate for finding such vortex solutions would be an SU(N) gauge theory with adjoint representation Higgs bosons. Vortex solutions in nonabelian Higgs t...

Vortex solutions in nonabelian Higgs theories

Physics Letters B, 2000

A new class of vortex solutions is found in SU (2) gauge theories with two adjoint representation Higgs bosons. Implications of these new solutions and their possible connection with Center Gauge fixed pure gauge theories are discussed.

Non-Abelian Multiple Vortices in Supersymmetric Field Theory

Communications in Mathematical Physics, 2011

In this paper, we consider a system of non-Abelian multiple vortex equations governing coupled SU (N ) and U (1) gauge and Higgs fields which may be embedded in a supersymmetric field theory framework. When the underlying domain is doubly periodic, we prove the existence and uniqueness of an n-vortex solution under a necessary and sufficient condition explicitly relating the domain size to the vortex number n and the Higgs boson masses. When the underlying domain is the full plane, we use a constructive approach to establish the existence and uniqueness of an n-vortex solution.

Effective Action of Non-Abelian Monopole-Vortex Complex

2012

We construct effective actions for non-Abelian 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) monopole-vortex complexes in 4d N = 2 supersymmetric gauge theories with gauge groups U (N ), U (1) × SO(2n) and U (1) × U Sp(2n). In the color-flavor locked vacuum with degenerate hypermultiplet masses, a subgroup of the color-flavor diagonal symmetry remains unbroken and gives internal orientational moduli to vortices which confine monopoles in the Higgs phase. In this paper we discuss the effective action which describes the interactions between monopoles and the orientational moduli of non-Abelian vortices both from the bulk and vortex worldsheet theories. In the large mass limit, we find that the effective action consists of two-dimensional non-linear sigma models on vortex worldsheets and boundary terms which describes monopole-vortex interactions.

A topological field theory for non-abelian vortices

Physics Letters B, 1990

We construct a two-dimensional topological field theory for non-abelian Higgs vortices. We discuss relevant features of the resulting BRST quantized theory and also discuss topological invariants.

Novel spin and statistical properties of nonabelian vortices

Physics Letters B, 1993

We study the statistics of vortices which appear in (2 + 1)-dimensional spontaneously broken gauge theories, where a compact group G breaks to a finite nonabelian subgroup H. Two simple models are presented. In the first, a quantum state which is symmetric under the interchange of a pair of indistinguishable vortices can be transformed into an antisymmetric state after the passage through the system of a third vortex with an appropriate H-flux element. Further, there exist states containing two indistinguishable spinless vortices which obey Fermi statistics. These results generalize to loops of nonabelian cosmic string in 3+1 dimensions. In the second model, fractional analogues of the above behaviors occur. Also, composites of vortices in this theory may possess fractional "Cheshire spin" which can be changed by passing an additional vortex through the system.

Massive Quantum Vortex Excitations in a Pure Gauge Abelian Theory in 2 + 1D

International Journal of Modern Physics A, 1997

We introduce and study a pure gauge Abelian theory in 2 + 1D in which massive quantum vortex states do exist in the spectrum of excitations. This theory can be mapped in a three-dimensional gas of point particles with a logarithmic interaction, in the grand-canonical ensemble. We claim that this theory is the 2 + 1D analog of the sine–Gordon, the massive vortices being the counterparts of sine–Gordon solitons. We show that a symmetry breaking, order parameter, similar to the vacuum expectation value of a Higgs field does exist.

Vortex description of the first-order phase transition in the two-dimensional Abelian-Higgs model

Physical Review E, 2003

We use both analytical arguments and detailed numerical evidence to show that the first-order transition in the type-I two-dimensional Abelian-Higgs model is commensurate with the statistical behavior of its vortex fluctuations, which behave as an ensemble of attractive particles. The clustering instabilities of such ensembles are shown to be connected to the process of phase nucleation. Calculations of the vortex equation of state show that the temperature for the onset of clustering is in qualitative agreement with the critical temperature. The vortex description provides a general gauge invariant mesoscopic mechanism for the first-order transition and applies for arbitrary type-I couplings.