Rigid open membrane and non-abelian non-commutative Chern-Simons theory
نویسنده
چکیده
In the Berkooz-Douglas matrix model of M theory in the presence of longitudinal M5-brane, we investigate the effective dynamics of the system by considering the longitudinal M5-brane as the background and the spherical M5-brane related with the other space dimensions as the probe brane. Due to there exists the background field strength provided by the source of the longitudinal M5-brane, an open membrane should be ended on the spherical M5-brane based on the topological reason. The formation of the bound brane configuration for the open membrane ending on the 5branes in the background of longitudinal 5-brane can be used to model the 4-dimensional quantum Hall system proposed recently by Zhang and Hu. The description of the excitations of the quantum Hall soliton brane configuration is established by investigating the fluctuations of D0-branes living on the bound brane around their classical solution derived by the transformations of area preserving diffeomorphisms of the open membrane. We find that this effective field theory for the fluctuations is an SO(4) non-commutative Chern-Simons field theory. The matrix regularized version of this effective field theory is given in order to allow the finite D0-branes to live on the bound brane. We also discuss some possible applications of our results to the related topics in M-theory and to the 4-dimensional quantum Hall system. PACS: 11.25.Yb, 11.10.Nx, 11.90.+t
منابع مشابه
Realizing the Quantum Hall System in String Theory
In a recent paper Bernevig, Brodie, Susskind and Toumbas constructed a brane realization of the Quantum Hall fluid. Since then it has been realized that the Quantum Hall system is very closely related to non–commutative Chern Simons theory and this suggests alternative brane constructions which we believe are more reliable and clear. In this paper a brane construction is given for the non–commu...
متن کاملSolitons in 2+1 Dimensional Non-Commutative Maxwell Chern-Simons Higgs Theories
We find soliton solutions in the 2+1 dimensional non-commutative Maxwell Chern-Simons Higgs theories. In the limit of the Chern-Simons coefficient going to zero, these solutions go over to the previously found solutions in the non-commutative Maxwell Higgs theories. The new solutions may have relevance in the theory of the fractional quantum Hall effect and possibly in string vacua correspondin...
متن کاملThe Quantum Hall Fluid and Non–Commutative Chern Simons Theory
The first part of this paper is a review of the author’s work with S. Bahcall which gave an elementary derivation of the Chern Simons description of the Quantum Hall effect for filling fraction 1/n. The notation has been modernized to conform with standard gauge theory conventions. In the second part arguments are given to support the claim that abelian non– commutative Chern Simons theory at l...
متن کاملEdge Currents in Non-commutative Chern-simons Theory from a New Matrix Model
This paper discusses the formulation of the non-commutative Chern-Simons (CS) theory where the spatial slice, an infinite strip, is a manifold with boundaries. As standard ∗products are not correct for such manifolds, the standard non-commutative CS theory is not also appropriate here. Instead we formulate a new finite-dimensional matrix CS model as an approximation to the CS theory on the stri...
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 کامل