Dually-charged mesoatom on the space of constant negative curvature

The discrete spectrum solutions corresponding to dually-charged mesoatom on the space of constant negative curvature are obtained. The discrete spectrum of energies is finite and vanishes, when the magnetic charge of the nucleus exceeds the critical value.Comment: 15 pages, LaTe

On the "scattering law" for Kasner parameters in the model with one-component anisotropic fluid

A multidimensional cosmological type model with 1-component anisotropic fluid is considered. An exact solution is obtained. This solution is defined on a product manifold containing n Ricci-flat factor spaces. We singled out a special solution governed by the function cosh. It is shown that this special solution has Kasner-like asymptotics in the limits \tau \to + 0 and \tau \to + \infty, where \tau is a synchronous time variable. A relation between two sets of Kasner parameters \alpha_{\infty} and \alpha_{0} is found. This formula (of "scattering law") is coinciding with that obtained earlier for the S-brane solution (when scalar fields are absent).Comment: 23 pages, 1 figure, Late

On skew tau-functions in higher spin theory

Recent studies of higher spin theory in three dimensions concentrate on Wilson loops in Chern-Simons theory, which in the classical limit reduce to peculiar corner matrix elements between the highest and lowest weight states in a given representation of SL(N). Despite these "skew" tau-functions can seem very different from conventional ones, which are the matrix elements between the two highest weight states, they also satisfy the Toda recursion between different fundamental representations. Moreover, in the most popular examples they possess simple representations in terms of matrix models and Schur functions. We provide a brief introduction to this new interesting field, which, after quantization, can serve as an additional bridge between knot and integrability theories.Comment: 36 page

Exact solutions in multidimensional gravity with antisymmetric forms

This topical review deals with a multidimensional gravitational model containing dilatonic scalar fields and antisymmetric forms. The manifold is chosen in the form M = M_0 x M_1 x ...x M_n, where M_i are Einstein spaces (i >0). The sigma-model approach and exact solutions in the model are reviewed and the solutions with p-branes (e.g. Majumdar-Papapetrou-type, cosmological, spherically symmetric, black-brane and Freund-Rubin-type ones) are considered.Comment: 63 pages, Latex, topical review, few typos are eliminate