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

Holographic Coulomb Branch Flows with N=1 Supersymmetry

We obtain a large, new class of N=1 supersymmetric holographic flow backgrounds with U(1)^3 symmetry. These solutions correspond to flows toward the Coulomb branch of the non-trivial N=1 supersymmetric fixed point. The massless (complex) chiral fields are allowed to develop vevs that are independent of their two phase angles, and this corresponds to allowing the brane to spread with arbitrary, U(1)^2 invariant, radial distributions in each of these directions. Our solutions are "almost Calabi-Yau:" The metric is hermitian with respect to an integrable complex structure, but is not Kahler. The "modulus squared" of the holomorphic (3,0)-form is the volume form, and the complete solution is characterized by a function that must satisfy a single partial differential equation that is closely related to the Calabi-Yau condition. The deformation from a standard Calabi-Yau background is driven by a non-trivial, non-normalizable 3-form flux dual to a fermion mass that reduces the supersymmetry to N=1. This flux also induces dielectric polarization of the D3-branes into D5-branes.Comment: 22 pages; harvmac. Typos corrected;small improvements in presentatio

S-matrices for Perturbed N=2 Superconformal Field Theory from quantum groups

S-matrices for integrable perturbations of $N=2$ superconformal field theories are studied. The models we consider correspond to perturbations of the coset theory $G_k \times H_{g-h} /H_{k+g-h}$. The perturbed models are closely related to $\hat G$-affine Toda theories with a background charge tuned to $H$. Using the quantum group restriction of the affine Toda theories we derive the S-matrix.Comment: 29 pages 2 figure