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

On Heterotic/Type I Duality in d=8

We discuss heterotic corrections to quartic internal U(1) gauge couplings and check duality by calculating one-loop open string diagrams and identifying the D-instanton sum in the dual type I picture. We also compute SO(8)^4 threshold corrections and finally R^2 corrections in type I theory.Comment: 9 pages, Latex, To appear in the proceedings of "Quantum Aspects of Gauge Theories, Supersymmetries and Unification", Corfu, September 199

Free-field Representations and Geometry of some Gepner models

The geometry of $k^{K}$ Gepner model, where $k+2=2K$ is investigated by free-field representation known as "bc\bet\gm"-system. Using this representation it is shown directly that internal sector of the model is given by Landau-Ginzburg $\mathbb{C}^{K}/\mathbb{Z}_{2K}$-orbifold. Then we consider the deformation of the orbifold by marginal anti-chiral-chiral operator. Analyzing the holomorphic sector of the deformed space of states we show that it has chiral de Rham complex structure of some toric manifold, where toric dates are given by certain fermionic screening currents. It allows to relate the Gepner model deformed by the marginal operator to the $\sigma$-model on CY manifold realized as double cover of $\mathbb{P}^{K-1}$ with ramification along certain submanifold.Comment: LaTex, 14 pages, some acknowledgments adde

Synchrotron Mössbauer spectroscopic study of ferropericlase at high pressures and temperatures

The electronic spin state of Fe^(2+) in ferropericlase, (Mg_(0.75)Fe_(0.25))O, transitions from a high-spin (spin unpaired) to low-spin (spin paired) state within the Earth’s mid-lower mantle region. To better understand the local electronic environment of high-spin Fe^(2+) ions in ferropericlase near the transition, we obtained synchrotron Mössbauer spectra (SMS) of (Mg_(0.75),Fe_(0.25))O in externally heated and laser-heated diamond anvil cells at relevant high pressures and temperatures. Results show that the quadrupole splitting (QS) of the dominant high-spin Fe^(2+) site decreases with increasing temperature at static high pressure. The QS values at constant pressure are fitted to a temperature-dependent Boltzmann distribution model, which permits estimation of the crystal-field splitting energy (Δ_3) between the d_(xy_ and d_(xz) or d_(zy) orbitals of the t_(2g) states in a distorted octahedral Fe^(2+) site. The derived Δ_3 increases from approximately 36 meV at 1 GPa to 95 meV at 40 GPa, revealing that both high pressure and high temperature have significant effects on the 3d electronic shells of Fe^(2+) in ferropericlase. The SMS spectra collected from the laser-heated diamond cells within the time window of 146 ns also indicate that QS significantly decreases at very high temperatures. A larger splitting of the energy levels at high temperatures and pressures should broaden the spin crossover in ferropericlase because the degeneracy of energy levels is partially lifted. Our results provide information on the hyperfine parameters and crystal-field splitting energy of high-spin Fe^(2+) in ferropericlase at high pressures and temperatures, relevant to the electronic structure of iron in oxides in the deep lower mantle

Topological Matter, Integrable Models and Fusion Rings

We show how topological $G_k/G_k$ models can be embedded into the topological matter models that are obtained by perturbing the twisted $N=2$ supersymmetric, hermitian symmetric, coset models. In particular, this leads to an embedding of the fusion ring of $G$ as a sub-ring of the perturbed, chiral primary ring. The perturbation of the twisted $N=2$ model that leads to the fusion ring is also shown to lead to an integrable $N=2$ supersymmetric field theory when the untwisted $N=2$ superconformal field theory is perturbed by the same operator and its hermitian conjugate.Comment: 24 page

Differential Equations for Periods and Flat Coordinates in Two Dimensionsional Topological Matter Theories

We derive directly from the N=2 LG superpotential the differential equations that determine the flat coordinates of arbitrary topological CFT's.Comment: 34

Heterotic/type I duality, D-instantons and an N=2 AdS/CFT correspondence

D-instanton effects are studied for the IIB orientifold T^2/I\Omega(-1)^{F_L} of Sen using type I/heterotic duality. An exact one loop threshold calculation of t_8 \tr F^4 and t_8(\tr F^2)^2 terms for the heterotic string on T^2 with Wilson lines breaking SO(32) to SO(8)^4 is related to D-instanton induced terms in the worldvolume of D7 branes in the orientifold. Introducing D3 branes and using the AdS/CFT correspondence in this case, these terms are used to calculate Yang-Mills instanton contributions to four point functions of the large N_c limit of N=2 USp(2N_c) SYM with four fundamental and one antisymmetric tensor hypermultiplets.Comment: 25 pages, harvmac(b), one figure, v2: minor changes, version to appear in PR

The matrix factorisations of the D-model

The fundamental matrix factorisations of the D-model superpotential are found and identified with the boundary states of the corresponding conformal field theory. The analysis is performed for both GSO-projections. We also comment on the relation of this analysis to the theory of surface singularities and their orbifold description.Comment: 23 pages, LaTe

Lattice Analogues of N=2N=2 Superconformal Models via Quantum Group Truncation

We obtain lattice models whose continuum limits correspond to $N=2$ superconformal coset models. This is done by taking the well known vertex model whose continuum limit is the $G \times G/G$ conformal field theory, and twisting the transfer matrix and modifying the quantum group truncation. We find that the natural order parameters of the new models are precisely the chiral primary fields. The integrable perturbations of the conformal field theory limit also have natural counterparts in the lattice formulation, and these can be incorporated into an affine quantum group structure. The topological, twisted $N=2$ superconformal models also have lattice analogues, and these emerge as an intermediate part of our analysis.Comment: 25 pages and 2 figure