Quantization and eigenvalue distribution of noncommutative scalar field theory

The quantization of noncommutative scalar field theory is studied from the matrix model point of view, exhibiting the significance of the eigenvalue distribution. This provides a new framework to study renormalization, and predicts a phase transition in the noncommutative \phi^4 model. In 4-dimensions, the corresponding critical line is found to terminate at a non-trivial point.Comment: Talk presented at the II. Southeastern European Workshop BW 2005, Vrnjacka Banja, Serbia and the XIV. Workshop of Geometric Methods in Physics, Bialowieza, Poland. To appear in Facta Universitati

Finite dimensional unitary representations of quantum Anti-de Sitter groups at roots of unity

We study irreducible unitary \reps of $U_q(SO(2,1))$ and $U_q(SO(2,3))$ for $q$ a root of unity, which are finite dimensional. Among others, unitary \reps corresponding to all classical one-particle representations with integral weights are found for $q = e^{i \pi /M}$, with $M$ being large enough. In the "massless" case with spin bigger than or equal to 1 in 4 dimensions, they are unitarizable only after factoring out a subspace of "pure gauges", as classically. A truncated associative tensor product describing unitary many-particle representations is defined for $q = e^{i\pi /M}$.Comment: More systematic proof of statements on the structure of irreps, some typos corrected. 25 pages LaTeX, 4 figures included using epsf. To appear in Comm. Math. Phy

One-loop stabilization of the fuzzy four-sphere via softly broken SUSY

We describe a stabilization mechanism for fuzzy $S^4_N$ in the Euclidean IIB matrix model due to vacuum energy in the presence of a positive mass term. The one-loop effective potential for the radius contains an attractive contribution attributed to supergravity, while the mass term induces a repulsive contribution for small radius due to SUSY breaking. This leads to a stabilization of the radius. The mechanism should be pertinent to recent results on the genesis of 3+1-dimensional space-time in the Minkowskian IIB model.Comment: 28 pages, 3 figures. V2: typos fixed, improved discussion, published version. V3,V4: reference adde

Quantized open FRW cosmology from Yang-Mills matrix models

We present simple solutions of IKKT-type matrix models describing a quantized homogeneous and isotropic cosmology with $k=-1$, finite density of microstates and a resolved Big Bang. At late times, a linear coasting cosmology $a(t) \propto t$ is obtained, which is remarkably close to observation. The solution consists of two sheets with opposite intrinsic chiralities, which are connected in a Euclidean pre-big bang era.Comment: 5 pages, 1 figure. V2: minor correction