The CWKB approach to non-reflecting potential and cosmological implications

We discuss the method of calculating the reflection coefficient using complex trajectory WKB (CWKB) approximation. This enables us to give an interpretation of non-reflecting nature of the potential under certain conditions and clarify some points, reported incorrectly elsewhere [vs:ejp] for the potential $U(x)=-U_0cosh^2(x/a)$. We show that the repeated reflectios between the turning points are essential, which most authors overlooked, in obtaining the non-reflecting c ondition. We find that the considered repeated reflection paths are in conformity with Bogolubov transformation technique. We discuss the implications of the results when applied to the particle production scenario, considering $x$ as a time variable and also stress the cosmological implications of the result with reference to radiation domonated and de Sitter spacetime.Comment: 9 pages, late

Rationality and Brauer group of a moduli space of framed bundles

We prove that the moduli spaces of framed bundles over a smooth projective curve are rational. We compute the Brauer group of these moduli spaces to be zero under some assumption on the stability parameter.Comment: 7 pages, to appear in Tbilisi Math. J; v2. reference adde

The Topology of Parabolic Character Varieties of Free Groups

Let G be a complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectively, Y) be the space of equivalence classes of representations of the free group of m+n generators in G (respectively, K) such that for each i between 1 and m, the image of the i-th free generator is conjugate to h_i. These spaces are parabolic analogues of character varieties of free groups. We prove that Y is a strong deformation retraction of X. In particular, X and Y are homotopy equivalent. We also describe explicit examples relating X to relative character varieties.Comment: 16 pages, version 2 includes minor revisions and some modified proofs, accepted for publication in Geometriae Dedicat

Nonlocal Gravitational Models and Exact Solutions

A nonlocal gravity model with a function $f(\Box^{-1} R)$, where $\Box$ is the d'Alembert operator, is considered. The algorithm, allowing to reconstruct $f(\Box^{-1} R)$, corresponding to the given Hubble parameter and the state parameter of the matter, is proposed. Using this algorithm, we find the functions $f(\Box^{-1} R)$, corresponding to de Sitter solutions.Comment: 5 pages, v2: refs. added, to appear in the proceedings of the International Workshop "Supersymmetries and Quantum Symmetries" (SQS'2011), Dubna, Russia, July 18-23, 2011, http://theor.jinr.ru/sqs/2011

Finite Temperature Solitons in Non-Local Field Theories from p-Adic Strings

Non-local field theories which arise from p-adic string theories have vacuum soliton solutions. We find the soliton solutions at finite temperature. These solutions become important for the partition function when the temperature exceeds m_s/g_o^2 where m_s is the string mass scale and g_o is the open string coupling.Comment: 22 pages, 6 figure