The BRST quantization and the no-ghost theorem for AdS_3

In our previous papers, we prove the no-ghost theorem without light-cone directions (hep-th/0005002, hep-th/0303051). We point out that our results are valid for more general backgrounds. In particular, we prove the no-ghost theorem for AdS_3 in the context of the BRST quantization (with the standard restriction on the spin). We compare our BRST proof with the OCQ proof and establish the BRST-OCQ equivalence for AdS_3. The key in both approaches lies in the certain structure of the matter Hilbert space as a product of two Verma modules. We also present the no-ghost theorem in the most general form.Comment: 22 pages, JHEP and AMS-LaTeX; v2 & 3: minor improvement

Superstrings on NS5 backgrounds, deformed AdS3 and holography

We study a non-standard decoupling limit of the D1/D5-brane system, which interpolates between the near-horizon geometry of the D1/D5 background and the near-horizon limit of the pure D5-brane geometry. The S-dual description of this background is actually an exactly solvable two-dimensional (worldsheet) conformal field theory: {null-deformed SL(2,R)} x SU(2) x T^4 or K3. This model is free of strong-coupling singularities. By a careful treatment of the SL(2,R), based on the better-understood SL(2,R) / U(1) coset, we obtain the full partition function for superstrings on SL(2,R) x SU(2) x K3. This allows us to compute the partition functions for the J^3 and J^2 current-current deformations, as well as the full line of supersymmetric null deformations, which links the SL(2,R) conformal field theory with linear dilaton theory. The holographic interpretation of this setup is a renormalization-group flow between the decoupled NS5-brane world-volume theory in the ultraviolet (Little String Theory), and the low-energy dynamics of super Yang--Mills string-like instantons in six dimensions.Comment: JHEP style, 59 pages, 1 figure; v2: minor changes, to appear in JHE

Glassy Random Matrix Models

This paper discusses Random Matrix Models which exhibit the unusual phenomena of having multiple solutions at the same point in phase space. These matrix models have gaps in their spectrum or density of eigenvalues. The free energy and certain correlation functions of these models show differences for the different solutions. Here I present evidence for the presence of multiple solutions both analytically and numerically. As an example I discuss the double well matrix model with potential $V(M)= -{\mu \over 2}M^2+{g \over 4}M^4$ where $M$ is a random $N\times N$ matrix (the $M^4$ matrix model) as well as the Gaussian Penner model with $V(M)={\mu\over 2}M^2-t \ln M$. First I study what these multiple solutions are in the large $N$ limit using the recurrence coefficient of the orthogonal polynomials. Second I discuss these solutions at the non-perturbative level to bring out some differences between the multiple solutions. I also present the two-point density-density correlation functions which further characterizes these models in a new university class. A motivation for this work is that variants of these models have been conjectured to be models of certain structural glasses in the high temperature phase.Comment: 25 pages, Latex, 7 Figures, to appear in PR