On Modified Gravity

We consider some aspects of nonlocal modified gravity, where nonlocality is of the type $R \mathcal{F}(\Box) R$. In particular, using ansatz of the form $\Box R = c R^\gamma,$ we find a few $R(t)$ solutions for the spatially flat FLRW metric. There are singular and nonsingular bounce solutions. For late cosmic time, scalar curvature R(t) is in low regime and scale factor a(t) is decelerated. R (t) = 0 satisfies all equations when k = -1.Comment: added references; made some clarifications; 8 page

Note on the Massive Rarita-Schwinger Field in the AdS/CFT correspondence

We consider a massive Rarita-Schwinger field on the Anti-de Sitter space and solve the corresponding equations of motion. We show that appropriate boundary terms calculated on-shell give two-point correlation functions for spin-3/2 fields of the conformal field theory on the boundary. The relation between Rarita-Schwinger field masses and conformal dimensions of corresponding operators is established.Comment: LaTeX, 10 page

Holographic thermalization from Kerr-AdS

Theoretical Physic

UV/IR Mixing for Noncommutative Complex Scalar Field Theory, II (Interaction with Gauge Fields)

We consider noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY Yang-Mills theory. We show that one-loop renormalizability of noncommutative scalar electrodynamics requires the scalar potential to be an anticommutator squared. This form of the scalar potential differs from the one expected from the point of view of noncommutative gauge theories with extended SUSY containing a square of commutator. We show that fermion contributions restore the commutator in the scalar potential. This provides one-loop renormalizability of noncommutative N=2 SUSY gauge theory. We demonstrate a presence of non-integrable IR singularities in noncommutative scalar electrodynamics for general coupling constants. We find that for a special ratio of coupling constants these IR singularities vanish. Also we show that IR poles are absent in noncommutative N=2 SUSY gauge theory.Comment: 9 pages, 16 EPS figure

Tachyon condensation in cubic superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the non-BPS D-brane or brane-anti-D-brane pair, the negative energy density cancels the brane tension. We study this conjecture using a cubic superstring field theory with insertion of a double-step inverse picture changing operator. We compute the tachyon potential at levels (1/2,1) and (2,6). In the first case we obtain that the value of the potential at the minimum is 97.5% of the non BPS D-brane tension. Using a special gauge in the second case we get 105.8% of the tension.Comment: 19 pages, LaTeX, 3 figures. Eqs. (3.2), (3.3) and (4.6) are corrected, and new gauge fixing condition is use

THE CRITICAL DEPTH OF A NON-PROPAGATING FATIGUE CRACK AND THE REGULIARITIES OF ITS FORMATION

The dependence of the stresses intencity coefficient on the cylindrical parts crack depth has been examined. The connection between the critical depth of a non-propagating fatigue crack and the stresses intencity coefficient has been stated

On Stable Sector in Supermembrane Matrix Model

We study the spectrum of SU(2) x SO(2) matrix supersymmetric quantum mechanics. We use angular coordinates that allow us to find an explicit solution of the Gauss law constraints and single out the quantum number n (the Lorentz angular momentum). Energy levels are four-fold degenerate with respect to n and are labeled by n_q, the largest n in a quartet. The Schr\"odinger equation is reduced to two different systems of two-dimensional partial differential equations. The choice of a system is governed by n_q. We present the asymptotic solutions for the systems deriving thereby the asymptotic formula for the spectrum. Odd n_q are forbidden, for even n_q the spectrum has a continuous part as well as a discrete one, meanwhile for half-integer n_q the spectrum is purely discrete. Taking half-integer n_q one can cure the model from instability caused by the presence of continuous spectrum.Comment: 29 pages, 5 figure

Gauge Invariance and Tachyon Condensation in Cubic Superstring Field Theory

The gauge invariance of cubic open superstring field theory is considered in a framework of level truncation, and applications to the tachyon condensation problem are discussed. As it is known, in the bosonic case the Feynman-Siegel gauge is not universal within the level truncation method. We explore another gauge that is more suitable for calculation of the tachyon potential for fermionic string at level (2,6). We show that this new gauge has no restrictions on the region of its validity at least at this level.Comment: 21 pages, 2 figures, LaTeX 2e; references added, typos correcte