Representation of SU(infinity) Algebra for Matrix Models

We investigate how the matrix representation of SU(N) algebra approaches that of the Poisson algebra in the large N limit. In the adjoint representation, the (N^2-1) times (N^2-1) matrices of the SU(N) generators go to those of the Poisson algebra in the large N limit. However, it is not the case for the N times N matrices in the fundamental representation.Comment: 8 page

Space-time non-commutativity tends to create bound states

We study the spectrum of fluctuations about static solutions in 1+1 dimensional non-commutative scalar field models. In the case of soliton solutions non-commutativity leads to creation of new bound states. In the case of static singular solutions an infinite tower of bound states is produced whose spectrum has a striking similarity to the spectrum of confined quark states.Comment: revtex4, 6 pages, v2: a reference adde

On plane wave and vortex-like solutions of noncommutative Maxwell-Chern-Simons theory

We investigate the spectrum of the gauge theory with Chern-Simons term on the noncommutative plane, a modification of the description of the Quantum Hall fluid recently proposed by Susskind. We find a series of the noncommutative massive ``plane wave'' solutions with polarization dependent on the magnitude of the wave-vector. The mass of each branch is fixed by the quantization condition imposed on the coefficient of the noncommutative Chern-Simons term. For the radially symmetric ansatz a vortex-like solution is found and investigated. We derive a nonlinear difference equation describing these solutions and we find their asymptotic form. These excitations should be relevant in describing the Quantum Hall transitions between plateaus and the end transition to the Hall Insulator.Comment: 17 pages, LaTeX (JHEP), 1 figure, added references, version accepted to JHE

Noncommutative Self-dual Gravity

Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use Seiberg-Witten map. It is shown that the noncommutative torsion constraint is solved by the vanishing of commutative torsion. Finally, the noncommutative corrections to the action are computed up to second order.Comment: 15+1 pages, LaTeX, no figure

Anomalies, Fayet-Iliopoulos terms and the consistency of orbifold field theories

We study the consistency of orbifold field theories and clarify to what extent the condition of having an anomaly-free spectrum of zero-modes is sufficient to guarantee it. Preservation of gauge invariance at the quantum level is possible, although at the price, in general, of introducing operators that break the 5d local parity. These operators are, however, perfectly consistent with the orbifold projection. We also clarify the relation between localized Fayet-Iliopoulos (FI) terms and anomalies. These terms can be consistently added, breaking neither local supersymmetry nor the gauge symmetry. In the framework of supergravity the localized FI term arises as the boundary completion of a bulk interaction term: given the bulk Lagrangian the FI is fixed by gauge invariance.Comment: 31 pages, 1 figure. v2: some typos corrected, references adde

Noncommutative Topological Theories of Gravity

The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler characteristic and the signature invariant are obtained. This gives us a way towards the description of noncommutative gravitational instantons as well as noncommutative local gravitational anomalies.Comment: 17+1 pages, LaTeX, no figures, some clarifications, comments and references added, style improve

Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation

We continue our investigation of the phenomenological implications of the "deformed" commutation relations [x_i,p_j]=i hbar[(1 + beta p^2) delta_{ij} + beta' p_i p_j]. These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relation which appears in perturbative string theory. In this paper, we consider the effects of the deformation on the classical orbits of particles in a central force potential. Comparison with observation places severe constraints on the value of the minimum length.Comment: 20 pages REVTEX4, 4 color eps figures, typos correcte

Vertex Ring-Indexed Lie Algebras

Infinite dimensional Lie algebras are introduced, which are only partially graded, and are specified by indices lying on cyclotomic rings. They may be thought of as generalisations of the Onsager algebra, but unlike it or its sl(n) generalisations, they are not subalgebras of loop algebras associated with sln(n). In a particularly interesting ase associalte with sl(3), their indices lie on the Eisenstein integer triangular lattice and these algebras are expected to undelie vertex operator combinations in CFT, brane physics and graphite monolayers

Deforming maps for quantum algebras

We find explicit functionals that map SU(2) algebra generators to those of several quantum deformations of that algebra, as well as their SU(1, 1) analogs. We explain how any such quantized algebra can be mapped to any other, and how representations of any such algebra can be expressed as simple functions of SU(2) representations. We also discuss comultiplication rules, and explore quantum deformations of the Virasoro algebra

Geometrostasis and torsion in covariant superstrings

We give a geometric argument to understand the relative strength of the metric and torsion terms that constitute the covariant actions for freely propagating superstrings. We show the relative strength is precisely that for which the torsion flattens the underlying superspace manifold, i.e. for which geometrostasis occurs, thereby yielding trivially integrable systems on the world-sheet, in complete analogy with conventional two-dimensional σ-models. We fully discuss free heterotic superstrings, and give partial results for N = 2 superstrings