An N=1 Supersymmetric Coulomb Flow

We find a three-parameter family of solutions to IIB supergravity that corresponds to N=1 supersymmetric holographic RG flows of N=4 supersymmetric Yang Mills theory. This family of solutions allows one to give a mass to a single chiral superfield, and to probe a two-dimensional subspace of the Coulomb branch. In particular, we examine part of the Coulomb branch of the Leigh-Strassler fixed point. We look at the infra-red asymptotics of these flows from the ten-dimensional perspective. We also make general conjectures for the lifting Ansatz of five-dimensional scalar configurations to ten-dimensional tensor gauge fields. Our solution provides a highly non-trivial test of these conjectures.Comment: 13 pages; harvma

The deformed Virasoro algebra at roots of unity

We discuss some aspects of the representation theory of the deformed Virasoro algebra \virpq. In particular, we give a proof of the formula for the Kac determinant and then determine the center of \virpq for $q$ a primitive N-th root of unity. We derive explicit expressions for the generators of the center in the limit $t=qp^{-1}\to \infty$ and elucidate the connection to the Hall-Littlewood symmetric functions. Furthermore, we argue that for q=\sqrtN{1} the algebra describes `Gentile statistics' of order $N-1$, i.e., a situation in which at most $N-1$ particles can occupy the same state.Comment: 51 pages, TeX (with amssym.def

On deformed W-algebras and quantum affine algebras

We discuss some aspects of the deformed W-algebras W_{q,t}[g]. In particular, we derive an explicit formula for the Kac determinant, and discuss the center when t^2 is a primitive k-th root of unity. The relation of the structure of W_{q,t}[g] to the representation ring of the quantum affine algebra U_q(\hat g), as discovered recently by Frenkel and Reshetikhin, is further elucidated in some examples.Comment: 40 pages, plain TeX with amssym.def, improved referencin

Flavor meson localization in 5d braneworld

We propose a brane-world, which contains flavor quarks and mesons, by embedding dimensionally reduced D7-brane in both the supersymmetric and non-supersymmetric 5d background which are obtained as the solutions of type IIB supergravity compactified on Ad$S_5\times S^5$. In the supersymmetric case, the RS brane can be put at any point of the fifth coordinate, but it is pushed to the Ad$S_5$ boundary in the non-supersymmetric case. We study the localization of the flavor mesons, the fluctuation-modes of D7-brane, on the Randall-Sundrum brane in these backgrounds.Comment: 15 pages, 2 figure