A Class of Distal Functions on Semitopological Semigroups

The norm closure of the algebra generated by the set $\{n\mapsto {\lambda}^{n^k}:$ $\lambda\in{\mathbb {T}}$ and $k\in{\mathbb{N}}\}$ of functions on $({\mathbb {Z}}, +)$ was studied in \cite{S} (and was named as the Weyl algebra). In this paper, by a fruitful result of Namioka, this algebra is generalized for a general semitopological semigroup and, among other things, it is shown that the elements of the involved algebra are distal. In particular, we examine this algebra for $({\mathbb {Z}}, +)$ and (more generally) for the discrete (additive) group of any countable ring. Finally, our results are treated for a bicyclic semigroup.Comment: To appear in Methods Funct. Anal. Topolog

Different D-brane Interactions

We use rotation of one D-brane with respect to the other to reveal the hidden structure of D-branes in type-II theories. This is done by calculation of the interaction amplitude for two different parallel and angled branes. The analysis of strings with different boundary conditions at the ends is also given. The stable configuration for two similar branes occurs when they are anti-parallel. For branes of different dimensions stability is attained for either parallel or anti-parallel configurations and when dimensions differ by four the amplitude vanishes at the stable point. The results serve as more evidence that D-branes are stringy descriptions of non-perturbative extended solutions of SUGRA theories, as low energy approximation of superstrings.Comment: Tex, 12 pages. Typographical errors are corrected, minor changes done, acknowledgements adde

Horizon fluff, semi-classical black hole microstates - Log-corrections to BTZ entropy and black hole/particle correspondence

According to the horizon fluff proposal microstates of a generic black hole belong to a certain subset of near horizon soft hairs that cannot be extended beyond the near horizon region. In [1,2] it was shown how the horizon fluff proposal works for AdS3 black holes. In this work we clarify further this picture by showing that BTZ black hole microstates are in general among the coherent states in the Hilbert space associated with conic spaces or their Virasoro descendants, provided we impose a (Bohr-type) quantization condition on the angular deficit. Thus BTZ black holes may be viewed as condensates (or solitonic states) of AdS3 particles. We provide canonical and microcanonical descriptions of the statistical mechanical system associated with BTZ black holes and their microstates, and relate them. As a further non-trivial check we show the horizon fluff proposal correctly reproduces the expected logarithmic corrections to the BTZ entropy.Comment: 47pp, v2: added references, minor correction in section 6.1, results unchanged, v3: 51pp, added figures, references and clarifications, to appear in JHE

On Classification of Geometries with SO(2,2) Symmetry

Motivated by the Extremal Vanishing Horizon (EVH) black holes, their near horizon geometry and the EVH/CFT proposal, we construct and classify solutions with (local) SO(2,2) symmetry to four and five dimensional Einstein-Maxwell-Dilaton (EMD) theory with positive, zero or negative cosmological constant Lambda, the EMD-$\Lambda$ theory, and also $U(1)^4$ gauged supergravity in four dimensions and $U(1)^3$ gauged supergravity in five dimensions. In four dimensions the geometries are warped product of AdS3 with an interval or a circle. In five dimensions the geometries are of the form of warped product of AdS3 and a 2d surface $\Sigma_2$. For the Einsten-Maxwell-$\Lambda$ theory we prove that $\Sigma_2$ should have a U(1) isometry, a rigidity theorem in this class of solutions. We also construct all d dimensional Einstein vacuum solutions with $SO(2,2) \times U(1)^{d-4}$ or $SO(2,2) \times SO(d-3)$ isometry.Comment: 26 pages, updated to published versio