Abstract:
In this letter the boundary problem for massless and massive Rarita-Schwinger field in the AdS/CFT correspondence is considered. The considerations are along the lines of a paper by Henneaux (hep-th/9902137) and are based on the requirement the solutions to be a stationary point for the action functional. It is shown that this requirement, along with a definite asymptotic behavior of the solutions, fixes the boundary term that must be added to the initial Rarita-Schwinger action. It is also shown that the boundary term reproduce the known two point correlation functions of certain local operators in CFT living on the boundary.

Abstract:
In a recent paper Klebanov and Witten (hep-th/9905104) proposed to formulate the AdS/CFT correspondence principle by taking an "irregular boundary condition" for a scalar field. In this paper we generalize this idea to the case of spinor field with interaction. The action functional following from the choice of irregular boundary conditions and which must be used in the AdS/CFT correspondence is related to the usual action by a Legendre transform. For the new theory we found the modified Green's function that must be used for internal lines in calculating higher order graphs. It is proved that the considerations are valid to all orders in perturbation theory.

Abstract:
We study the class of pulsating strings on AdS4×ℂℙ3. Using a generalized ansatz for pulsating string configurations we find new solutions of this class. Further we quasiclassically quantize the theory and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual 𝒩=6 Chern-Simons theory.

Abstract:
In this letter we propose exact three-point correlation functions for N=1 supersymmetric Liouville theory. Along the lines of Zamolodchikov and Zamolodchikov paper (hep-th/9506136) we propose a generalized special function which describe the three-point amplitudes. We consider briefly the so called reflection amplitudes in the supersymmetric case.

Abstract:
Some of the recent important developments in understanding string/ gauge dualities are based on the idea of highly symmetric motion of ``string solitons'' in $AdS_5\times S^5$ geometry originally suggested by Gubser, Klebanov and Polyakov. In this paper we study symmetric motion of short strings in the presence of antisymetric closed string B field. We compare the values of the energy and the spin in the case of non-vanishing B field with those obtained in the case of B=0. The presence of NS-NS antisymmetric field couples the fluctuation modes that indicates changes in the quantum corrections to the energy spectrum.

Abstract:
In the present paper we study SU(N)->S(U(N/2)xU(N/2)) symmetry breaking in N=4 SYM via AdS/CFT correspondence. We consider two stacks of N/2 parallel D3 branes separated by a distance 2\vec d. In this case there is mixing between the different l-wave dilatonic KK modes. We calculate certain the two point correlation functions in the dual gauge theory. Due to mode mixing, the diagonal correlation functions have 1/N conformal-like correction as well as deformation terms. The off-diagonal correlators are also non-vanishing and their leading order is 1/N. We discuss briefly the spectrum of the glueball exitations.

Abstract:
Some of the recent important developments in understanding string/ gauge dualities are based on the idea of highly symmetric motion of ``string solitons'' in $AdS_5\times S^5$ geometry originally suggested by Gubser, Klebanov and Polyakov. In this paper we study symmetric motion of certain string configurations in so called Pilch-Warner geometry. The two-form field $A_2$ breaks down the supersymmetry to $\mathcal{N}=1$ but for the string configurations considered in this paper the classical values of the energy and the spin are the same as for string in $AdS\times S^5$. Although trivial at classical level, the presence of NS-NS antisymmetric field couples the fluctuation modes that indicates changes in the quantum corrections to the energy spectrum. We compare our results with those obtained in the case of pp-wave limit in hep-th/0206045.

Abstract:
We consider tachyonic string-field fluctuations about a Dp-brane background in the geometrical (CFT) formulation of Vacuum String Field Theory. We then extend this analysis to the case of a background B-field. We find that the standard results for D-brane tension are reproduced in both cases.

Abstract:
Integrable hierarchy based on the constrained Osp(2$\mid%2) connection is considered. The connection with 2D supergravity and some analogies with the W$_3^{(2)}$ case are given. It is shown that super Virasoro transformations are symmetries of tha hierarchy.

Abstract:
We re-examine the recent proposal of Rastelli, Sen and Zwiebach on the tachyon fluctuation of the vacuum string field theory representing a D25 brane, originally considered by Hata and Kawano. We show that the tachyon state satisfies the linearized equations of motion on-shell in the strong sense thereby allowing us to calculate the ratio of energy density to the tension of the D-brane to be $E_c/T_{25}\simeq \pi^2/3[1/16(ln2)^3]\simeq 0.62$. Our proof relies on a careful handling of the limits ($n\to\infty$) involved in the conformal theory description of the sliver and tachyon states. We conjecture that the sliver state represents a single D25 brane.