The Refined Elliptic Genus and Coulomb Gas Formulations of N=2N=2 Superconformal Coset Models

We describe, in some detail, a number of different Coulomb gas formulations of $N=2$ superconformal coset models. We also give the mappings between these formulations. The ultimate purpose of this is to show how the Landau-Ginzburg structure of these models can be used to extract the $W$-generators, and to show how the computation of the elliptic genus can be refined so as to extract very detailed information about the characters of component parts of the model.Comment: 40 pages in harvmac, no figure

Investigating the BPS Spectrum of Non-Critical E_n Strings

We use the effective action of the $E_n$ non-critical strings to study its BPS spectrum for $0 \le n \le 8$. We show how to introduce mass parameters, or Wilson lines, into the effective action, and then perform the appropriate asymptotic expansions that yield the BPS spectrum. The result is the $E_n$ character expansion of the spectrum, and is equivalent to performing the mirror map on a Calabi-Yau with up to nine K\"ahler moduli. This enables a much more detailed examination of the $E_n$ structure of the theory, and provides extensive checks on the effective action description of the non-critical string. We extract some universal ($E_n$ independent) information concerning the degeneracies of BPS excitations.Comment: 50 pages, harvmac (b

Extended N=2 Superconformal Structure of Gravity and W-Gravity Coupled to Matter

We show that almost all string theories, including the bosonic string, the superstring and $W$-string theories, possess a twisted N=2 superconformal symmetry. This enables us to establish a connection between topological gravity and the field theoretical description of matter coupled to gravity. We also show how the \brs operators of the $W_n$-string can be obtained by hamiltonian reduction of $SL(n|n-1)$. The tachyonic and ground ring states of $W$-strings are described in the light of the N=2 superconformal structure, and the ground ring generators for the non-critical $W_3$-string are explicitly constructed. The relationship to $G/G$ models and quantum integrable systems is also briefly described.Comment: 48 page

Supersymmetric Randall-Sundrum Scenario

We present the supersymmetric version of the minimal Randall-Sundrum model with two opposite tension branes.Comment: Latex, 9 pages. Published versio

The complex geometry of holographic flows of quiver gauge theories

We argue that the complete Klebanov-Witten flow solution must be described by a Calabi-Yau metric on the conifold, interpolating between the orbifold at infinity and the cone over T^(1,1) in the interior. We show that the complete flow solution is characterized completely by a single, simple, quasi-linear, second order PDE, or "master equation," in two variables. We show that the Pilch-Warner flow solution is almost Calabi-Yau: It has a complex structure, a hermitian metric, and a holomorphic (3,0)-form that is a square root of the volume form. It is, however, not Kahler. We discuss the relationship between the master equation derived here for Calabi-Yau geometries and such equations encountered elsewhere and that govern supersymmetric backgrounds with multiple, independent fluxes.Comment: 26 pages, harvmac + amssy