Noncommutative Chern-Simons Solitons

Abstract

The Chern-Simons theories on a noncommutative plane, which is shown to be describing the quantum Hall liquid, is considered. We introduce matter fields fundamentally coupled to the noncommutative Chern-Simons field. Exploiting BPS equations for the nonrelativistic Chern-Simons theory, we find the exact solutions of multi vortices that are closely packed and exponentially localized. We determine the position, the size and the angular momentum explicitly. We then construct the solutions of two spatially separated vortices and determine the moduli dependence of the size and the angular momentum. We also consider the relativistic Chern-Simons theory and find nontopological solutions whose properties are similar to the nonrelativistic counterpart. However, unlike the nonrelativistic case, there are two branches of solutions for a given magnetic field and they cease to exist below certain noncommutativity scale.

16 pages, no figures, references added and typos corrected

References in corpus (10)

• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• BPS Bound States Of D0-D6 And D0-D8 Systems In A B-Field
• Noncommutative Vortex Solitons
• A Note on Noncommutative Chern-Simons Theories
• D-brane Dynamics and the Quantum Hall Effect
• Solitons in 2+1 Dimensional Non-Commutative Maxwell Chern-Simons Higgs Theories
• Nielsen-Olesen vortices in noncommutative space
• Self-dual Chern-Simons solitons in noncommutative space
• Comments on Noncommutative Gauge Theories
• Projector Equivalences in K theory and Families of Non-commutative Solitons

Cited by in corpus (26)

• Covariant Coordinate Transformations on Noncommutative Space
• Chern-Simons Theories on Noncommutative Plane
• Nonrelativistic anyons in external electromagnetic field
• Three-dimensional Noncommutative Gravity
• LLL vs. LLM: Half BPS Sector of N=4 SYM Equals to Quantum Hall System
• Exotic galilean symmetry and non-commutative mechanics
• NC Branes and Hierarchies in Quantum Hall Fluids
• Galilean noncommutative gauge theory: symmetries & vortices
• Issues of duality on non-commutative manifolds: the {\it non-equivalence} between self-dual and topologically massive models
• Anyons, group theory and planar physics
• Noncommutative Chern-Simons Soliton
• A new approach to the analysis of a noncommutative Chern-Simons theory
• Computing noncommutative Chern-Simons theory radiative corrections on the back of an envelope
• Moving vortices in noncommutative gauge theory
• NC Effective Gauge Model for Multilayer FQH States
• Troubles with Spacetime Noncommutative Theories: Tachyons or S-branes?
• Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
• Edge excitations of the Chern Simons matrix theory for the FQHE
• Noncommutative massive Thirring model in three-dimensional spacetime
• Noncommutative Fluids
• Solitons and Quasielectrons in the Quantum Hall Matrix Model
• Deformed "Commutative" Chern - Simons System
• Symmetries of field theories on the non-commutative plane
• About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane
• Chern-Simons Solitons, Chiral Model, and (affine) Toda Model on Noncommutative Space
• Noncommutative Relativistic U(N) Chern-Simons Solitons