Non-Abelian Chern-Simons Vortices
نویسندگان
چکیده
We consider the bosonic sector of a N = 2 supersymmetric Chern-Simons-Higgs theory in 2 + 1 dimensions. The gauge group is U(1) × SU(N) and has Nf flavors of fundamental matter fields. The model supports non-Abelian (axially symmetric) vortices when Nf ≥ N , which have internal (orientational) moduli. When Nf > N , the solutions acquire additional collective coordinates parameterizing their transverse size. We solve the BPS equations numerically and obtain local (Nf = N) and semi-local (Nf > N) string solutions. A CP N−1 low-energy effective action for the orientational moduli is obtained in both cases. In the semilocal case there is an additional term in the effective action induced by the transverse size moduli. We find such term in the limit of large transverse size, where exact solutions can be obtained analytically.
منابع مشابه
Vortices in (abelian) Chern-Simons gauge theory
The vortex solutions of various classical planar field theories with (abelian) Chern-Simons term are reviewed. Relativistic vortices, put forward by Paul and Khare, arise when the Abelian Higgs model is augmented with the Chern-Simons term. Adding a suitable sixth-order potential and turning off the Maxwell term provides us with pure Chern-Simons theory with both topological and non-topological...
متن کاملElectrically and magnetically charged vortices in the Chern–Simons–Higgs theory
In this paper, we prove the existence of finite-energy electrically and magnetically charged vortex solutions in the full Chern–Simons–Higgs theory, for which both the Maxwell term and the Chern–Simons term are present in the Lagrangian density. We consider both Abelian and non-Abelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constr...
متن کاملar X iv : 0 81 1 . 35 24 v 1 [ he p - th ] 2 1 N ov 2 00 8 Non Abelian Chern - Simons – Higgs solutions in 2 + 1 dimensions
Non Abelian vortices of a SU(2) Chern-Simons–Higgs theory in 2+1 dimensions are constructed numerically. They represent natural counterparts of the U(1) solutions considered by Hong, Kim and Pac, and, by Jackiw and Weinberg. The Abelian embeddings are identified, for all values of the Higgs selfinteraction strength ν, resulting in both attractive and repulsive phases. A detailed analysis of the...
متن کاملNon-Abelian Chern-Simons vortices with generic gauge groups
We study non-Abelian Chern-Simon BPS-saturated vortices enjoying N = 2 supersymmetry in d = 2 + 1 dimensions, with generic gauge groups of the form U(1) × G, with G being a simple group, allowing for orientational modes in the solutions. We will keep the group as general as possible and utilizing the powerful moduli matrix formalism to provide the moduli spaces of vortices and derive the corres...
متن کاملLectures on (abelian) Chern-Simons vortices
Various aspects including the construction and the symmetries of Abelian Chern-Simons vortices are reviewed. Extended version of the Lectures delivered at NIKHEF (Amsterdam), July 2006.
متن کاملThe Dynamics of Chern-Simons Vortices
We study vortex dynamics in three-dimensional theories with ChernSimons interactions. The dynamics is governed by motion on the moduli space M in the presence of a magnetic field. For Abelian vortices, the magnetic field is shown to be the Ricci form over M; for non-Abelian vortices, it is the first Chern character of a suitable index bundle. We derive these results by integrating out massive f...
متن کامل