Generating functionals of correlation functions of p-form currents in AdS/CFT correspondence

The generating functional of correlation functions of the currents corresponding to general massless $p$-form potential is calculated in $AdS/CFT$ correspondence of Maldacena. For this we construct the boundary-to-bulk Green's functions of $p$-form potentials. The proportional constant of the current-current correlation function, which is related to the central charge of the operator product expansion, is shown to be c=(d-p\over 2\pi^{d/2}) (\Gamma (d-p) \over \Gamma ({d\over 2}-p)). The result agrees with the known cases such as $p=1$ or 2.Comment: 1 + 12 pages(LaTeX). Ward identity problem clearfied with enlarged reference

Correlators of currents corresponding to the massive pp-form fields in AdS/CFT correspondence

By solving the equations of motion of massive $p$-form potential in Anti-de-Sitter space and using the $AdS/CFT$ correspondence of Maldacena, the generating functional of two-point correlation functions of the currents is obtained. When the mass parameter vanishes the result agrees with the known massless case.Comment: 1+12 pages. Sequel to hep-th/9809132(the massless case with different method

Time evolution of rolling tachyons for a brane-antibrane pair

A precise form of the time evolution of rolling tachyons corresponding to a brane-antibrane pair is investigated by solving the Hamiltonian equations of motion under the assumption that in a region far away from branes the tachyon vacuum is almost already achieved, even at the beginning of the rolling.Comment: 10 pages, 2 figures. Addition of references in v2, inclusion of more details in v

Non-hermitian quantum canonical variables and the generalized ladder operators

Quantum canonical transformations of the second kind and the non-Hermitian realizations of the basic canonical commutation relations are investigated with a special interest in the generalization of the conventional ladder operators. The opeator ordering problem is shown to be resolved when the non-Hermitian realizations for the canonical variables which can not be measured simultaneously with the energy are chosen for the canonical quantizations. Another merit of the non-Hermitian representations is that it naturally allows us to introduce the generalized ladder operators with which one can solve eigenvalue problems quite neatly

Scalar Field Theory in the AdS/CFT Correspondence Revisited

We consider the role of boundary conditions in the $AdS_{d+1}/CFT_{d}$ correspondence for the scalar field theory. Also a careful analysis of some limiting cases is presented. We study three possible types of boundary conditions, Dirichlet, Neumann and mixed. We compute the two-point functions of the conformal operators on the boundary for each type of boundary condition. We show how particular choices of the mass require different treatments. In the Dirichlet case we find that there is no double zero in the two-point function of the operator with conformal dimension $\frac{d}{2}$. The Neumann case leads to new normalizations for the boundary two-point functions. In the massless case we show that the conformal dimension of the boundary conformal operator is precisely the unitarity bound for scalar operators. We find a one-parameter family of boundary conditions in the mixed case. There are again new normalizations for the boundary two-point functions. For a particular choice of the mixed boundary condition and with the mass squared in the range $-d^2/4<m^2<-d^2/4+1$ the boundary operator has conformal dimension comprised in the interval $[\frac{d-2}{2}, \frac{d}{2}]$. For mass squared $m^2>-d^2/4+1$ the same choice of mixed boundary condition leads to a boundary operator whose conformal dimension is the unitarity bound.Comment: 22 pages, LaTeX, minor errors corrected, Conclusions and one reference added, final version to be published in Nucl. Phys.

Spinor Exchange in AdS_{d+1}

We explicitly calculate a Witten diagram with general spinor field exchange on $(d+1)$-dimensional Euclidean Anti-de Sitter space, which is necessary to evaluate four-point correlation functions with spinor fields when we make use of the AdS/CFT correspondence, especially in supersymmetric cases. We also show that the amplitude can be reduced to a scalar exchange amplitude. We discuss the operator product expansion of the dual conformal field theory by interpreting the short distance expansion of the amplitude according to the AdS/CFT correspondence.Comment: 20 pages, harvmac; typos corrected and some English expressions improved; final version to appear in Nucl. Phys.

Spinning deformations of the D1-D5 system and a geometric resolution of Closed Timelike Curves

The SO(4) isometry of the extreme Reissner-Nordstrom black hole of N=1, D=5 supergravity can be partly broken, without breaking any supersymmetry, in two different ways. The ``right'' solution is a rotating black hole (BMPV); the ``left'' is interpreted as a black hole in a Godel universe. In ten dimensions, both spacetimes are described by deformations of the D1-D5-pp-wave system with the property that the non-trivial Closed Timelike Curves of the five dimensional manifold are absent in the universal covering space of the ten dimensional manifold. In the decoupling limit, the BMPV deformation is normalizable. It corresponds to the vev of an IR relevant operator of dimension \Delta=1. The Godel deformation is sub-leading in \alpha' unless we take an infinite vorticity limit; in such case it is a non-normalizable perturbation. It corresponds to the insertion of a vector operator of dimension \Delta=5. Thus we conclude that from the dual (1+1)-CFT viewpoint the SO(4) R-symmetry is broken `spontaneously' in the BMPV case and explicitly in the Godel case.Comment: 20 pages, no figures, LaTeX; v2: Minor improvements, to appear in Nucl. Phys.