International Journal of Modern Physics A

We outline a brief description of noncommutative geometry and present some applications in string theory. We use the fuzzy torus as our guiding example.

Solutions to an infinite class of conformally flat 5D GR metrics are here derived. Since the standard 4D cosmological models (FRW solutions) can be embedded within a flat 5D manifold, such solutions may, then, be of cosmological interest. However, such conformally flat solutions have previously been derived dependent on t and ronly; independent of x⁵. To be able to further examine the results of such a 5D embedding, a more general solution should also depend on x⁵. Such solutions (5D conformally flat, dependent on t, r and x⁵) are here derived. An additional property of such solutions is that they turn out to be Riemann flat; that also is discussed.

The main BRST cohomological properties of a free, massless tensor field that transforms in an irreducible representation of GL(D,ℝ), corresponding to a rectangular, two-column Young diagram with k>2 rows are studied in detail. In particular, it is shown that any nontrivial co-cycle from the local BRST cohomology group H(s|d) can be taken to stop either at antighost number (k+1) or k, its last component belonging to the cohomology of the exterior longitudinal derivative H(γ) and containing nontrivial elements from the (invariant) characteristic cohomology H^inv (δ|d).

We propose a novel infinite-volume brane world scenario where we live on a noninflating spherical 3-brane, whose radius is somewhat larger than the present Hubble size, embedded in higher dimensional bulk. Once we include higher curvature terms in the bulk, we find completely smooth solutions with the property that the 3-brane world-volume is noninflating for a continuous range of positive values of the brane tension, that is, without fine-tuning. In particular, our solution, which is a near-BPS background with supersymmetry broken on the brane around TeV, is controlled by a single integration constant.

We study the interconnection between the finite projective modules for a fuzzy sphere, determined in a previous paper, and the matrix model approach, making clear the physical meaning of noncommutative topological configurations.

The cosmological term is formulated in the framework of the extended loop representation and its particularization from the extended loop to the loop representations is given. The properties of the Gauss self-linking number are investigated. It is shown that the phase factor of the Kauffman bracket satisfies the Mandelstam identities, the diffeomorphism constraint and the Hamiltonian constraint with the cosmological constant in the extended loop calculus.

Using the language of differential forms, the Kaluza–Klein theory in 4+1 dimensions is derived. This theory unifies electromagnetic and gravitational interactions in four dimensions when the extra space dimension is compactified. Without any ad hoc assumptions about the five-dimensional metric, the theory also contains a scalar field coupled to the other fields. By a conformal transformation the theory is transformed from the Jordan frame to the Einstein frame where the physical content is more manifest. Including a cosmological constant in the five-dimensional formulation, it is seen to result in an exponential potential for the scalar field in four dimensions. A similar potential is also found from the Casimir energy in the compact dimension. The resulting scalar field dynamics mimics realistic models recently proposed for cosmological quintessence.

We consider a spherical thick 3-brane immersed in a five-dimensional bulk space–time. We demonstrate how the thick brane equation of motion expanded in powers of the thickness of the brane can be obtained from the expected junction conditions on the boundaries of thick brane with the two embedding space–times. It is shown that the finite thickness corrections lead to a faster collapse of the brane in the vacuum.

In this paper we continue our study of the exact solution in open bosonic string field theory. We present new solution in the string field theory defined on the background corresponding to the boundary conformal field theory describing D25-brane. Then we will study the fluctuation modes around this solution and we determine their basic properties from the linearized equation of motion of the string field theory defined above the classical solution.