Multi-vortex solution in the Sutherland model

We consider the large-$N$ Sutherland model in the Hamiltonian collective-field approach based on the $1/N$ expansion. The Bogomol'nyi limit appears and the corresponding solutions are given by static-soliton configurations. They exist only for \l<1, i.e. for the negative coupling constant of the Sutherland interaction. We determine their creation energies and show that they are unaffected by higher-order corrections. For \l=1, the Sutherland model reduces to the free one-plaquette Kogut-Susskind model.Comment: Latex, using ioplppt.sty, 11 page

Homolumo Gap and Matrix Model

We discuss a dynamical matrix model by which probability distribution is associated with Gaussian ensembles from random matrix theory. We interpret the matrix M as a Hamiltonian representing interaction of a bosonic system with a single fermion. We show that a system of second-quantized fermions influences the ground state of the whole system by producing a gap between the highest occupied eigenvalue and the lowest unoccupied eigenvalue.Comment: 8 pages, 2 figure

Algebra of the observables in the Calogero model and in the Chern-Simons matrix model

The algebra of observables of an N-body Calogero model is represented on the S_N-symmetric subspace of the positive definite Fock space. We discuss some general properties of the algebra and construct four different realizations of the dynamical symmetry algebra of the Calogero model. Using the fact that the minimal algebra of observables is common to the Calogero model and the finite Chern-Simons (CS) matrix model, we extend our analysis to the CS matrix model. We point out the algebraic similarities and distinctions of these models.Comment: 24 pages, misprints corrected, reference added, final version, to appear in PR

Duality and quasiparticles in the Calogero-Sutherland model: Some exact results

The quantum-mechanical many-body system with the potential proportional to the pairwise inverse-square distance possesses a strong-weak coupling duality. Based on this duality, particle and/or quasiparticle states are described as SU(1,1) coherent states. The constructed quasiparticle states are of hierarchical nature.Comment: RevTeX, 10 page

A twisted look on kappa-Minkowski: U(1) gauge theory

Kappa-Minkowski space-time is an example of noncommutative space-time with potentially interesting phenomenological consequences. However, the construction of field theories on this space, although operationally well-defined, is plagued with ambiguities. A part of ambiguities can be resolved by clarifying the geometrical picture of gauge transformations on the kappa-Minkowski space-time. To this end we use the twist approach to construct the noncommutative U(1) gauge theory coupled to fermions. However, in this approach we cannot maintain the kappa-Poincar\'e symmetry; the corresponding symmetry of the twisted kappa-Minkowski space is the twisted igl(1,3) symmetry. We construct an action for the gauge and matter fields in a geometric way, as an integral of a maximal form. We use the Seiberg-Witten map to relate noncommutative and commutative degrees of freedom and expand the action to obtain the first order corrections in the deformation parameter.Comment: 24 pages, clarifications added, reference list updated, to appear in JHE

New varying speed of light theories

We review recent work on the possibility of a varying speed of light (VSL). We start by discussing the physical meaning of a varying $c$, dispelling the myth that the constancy of $c$ is a matter of logical consistency. We then summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz invariance; bimetric theories (where the speeds of gravity and light are not the same); locally Lorentz invariant VSL theories; theories exhibiting a color dependent speed of light; varying $c$ induced by extra dimensions (e.g. in the brane-world scenario); and field theories where VSL results from vacuum polarization or CPT violation. We show how VSL scenarios may solve the cosmological problems usually tackled by inflation, and also how they may produce a scale-invariant spectrum of Gaussian fluctuations, capable of explaining the WMAP data. We then review the connection between VSL and theories of quantum gravity, showing how ``doubly special'' relativity has emerged as a VSL effective model of quantum space-time, with observational implications for ultra high energy cosmic rays and gamma ray bursts. Some recent work on the physics of ``black'' holes and other compact objects in VSL theories is also described, highlighting phenomena associated with spatial (as opposed to temporal) variations in $c$. Finally we describe the observational status of the theory. The evidence is currently slim -- redshift dependence in the atomic fine structure, anomalies with ultra high energy cosmic rays, and (to a much lesser extent) the acceleration of the universe and the WMAP data. The constraints (e.g. those arising from nucleosynthesis or geological bounds) are tight, but not insurmountable. We conclude with the observational predictions of the theory, and the prospects for its refutation or vindication.Comment: Final versio