Exploring Lovelock theory moduli space for Schroedinger solutions

We look for Schroedinger solutions in Lovelock gravity in $D > 4$. We span the entire parameter space and determine parametric relations under which the Schroedinger solution exists. We find that in arbitrary dimensions pure Lovelock theories have Schroedinger solutions of arbitrary radius, on a co-dimension one locus in the Lovelock parameter space. This co-dimension one locus contains the subspace over which the Lovelock gravity can be written in the Chern-Simons form. Schroedinger solutions do not exist outside this locus and on this locus they exist for arbitrary dynamical exponent z. This freedom in z is due to the degeneracy in the configuration space. We show that this degeneracy survives certain deformation away from the Lovelock moduli space.Comment: 22 pages, Title changed, contents revised with focus on Schroedinger solutions, extra references added, to match with the version published in Nucl. Phys.

A Calogero-Sutherland Type Model For Branched Polymers

We show that a Calogero-Sutherland type model with anharmonic interactions of fourth and sixth orders leads to the matrix model corresponding to the branched polymers. We also show that by suitably modifying this model one can also obtain N-particle problems which are connected to matrix models corresponding to the pure gravity phase as well as corresponding to the transition point between the soap bubble and the branched polymer phase.Comment: 6 pages, no figure

Interpolating function and Stokes Phenomena

When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such interpolating functions and discuss their physical implications. We propose that the analytic structures of the interpolating functions provide information on analytic property and Stokes phenomena of the physical quantity, which we approximate by the interpolating functions. We explicitly check our proposal for partition functions of zero-dimensional $\varphi^4$ theory and Sine-Gordon model. In the zero dimensional Sine-Gordon model, we compare our result with a recent result from resurgence analysis. We also comment on construction of interpolating function in Borel plane.Comment: 21+6 pages, 16 figures; v2: minor corrections; v3: minor correction

Type IIB string theory on AdS_5 X T^{nn'}

We study \kk spectrum of type IIB string theory compactified on $AdS_5 \times T^{nn'}$ in the context of $AdS/CFT$ correspondence. We examine some of the modes of the complexified 2 form potential as an example and show that for the states at the bottom of the \kk tower the corresponding $d=4$ boundary field operators have rational conformal dimensions. The masses of some of the fermionic modes in the bottom of each tower as functions of the $R$ charge in the boundary conformal theory are also rational. Furthermore the modes in the bottom of the towers originating from $q$ forms on $T^{11}$ can be put in correspondence with the BRS cohomology classes of the $c=1$ non critical string theory with ghost number $q$. However, a more detailed investigation is called for, to clarify further the relation of this supergravity background with the $c=1$ strings.Comment: Plain Tex, 12 pages, (v2) minor typos corrected, version to appear in PLB. (v3) Problem in the format of titlepage fixe

A Number of Quasi-Exactly Solvable N-body Problems

We present several examples of quasi-exactly solvable $N$-body problems in one, two and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding polynomials form an orthogonal set and many of their properties are similar to those of the Bender-Dunne polynomials. We also discuss QES problems where the polynomials do not form an orthogonal set.Comment: 17pages, Revtex, no figur