Topological Strings from WZW Models

We show that the BRST structure of the topological string is encoded in the ``small'' $N=4$ superconformal algebra, enabling us to obtain, in a non-trivial way, the string theory from hamiltonian reduction of $A(1|1)$. This leads to the important conclusion that not only ordinary string theories, but topological strings as well, can be obtained, or even defined, by hamiltonian reduction from WZW models. Using two different gradations, we find either the standard $N=2$ minimal models coupled to topological gravity, or an embedding of the bosonic string into the topological string. We also comment briefly on the generalization to super Lie algebras $A(n|n)$.Comment: 14p, late

String Amplitudes and N=2, d=4 Prepotential in Heterotic K3 x T^2 Compactifications

For the gauge couplings, which arise after toroidal compactification of six-dimensional heterotic N=1 string theories from the T^2 torus, we calculate their one-loop corrections. This is performed by considering string amplitudes involving two gauge fields and moduli fields. We compare our results with the equations following from N=2 special geometry and the underlying prepotential of the theory. Moreover we find relations between derivatives of the N=2, d=4 prepotential and world-sheet tau-integrals which appear in various string amplitudes of any T^2-compactification.Comment: 28 TeX pages, uses harvmac, Final Version to appear in NP

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

Calculations for Mirror Symmetry with D-branes

We study normal functions capturing D-brane superpotentials on several one- and two-parameter Calabi-Yau hypersurfaces and complete intersections in weighted projective space. We calculate in the B-model and interpret the results using mirror symmetry in the large volume regime, albeit without identifying the precise A-model geometry in all cases. We identify new classes of extensions of Picard-Fuchs equations, as well as a novel type of topology changing phase transition involving quantum D-branes. A 4-d domain wall which is obtained in one region of closed string moduli space from wrapping a four-chain interpolating between two Lagrangian submanifolds is, for other values of the parameters, represented by a disk ending on a single Lagrangian.Comment: 42 page

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

Orientifolds, Unoriented Instantons and Localization

We consider world-sheet instanton effects in N=1 string orientifolds of noncompact toric Calabi-Yau threefolds. We show that unoriented closed string topological amplitudes can be exactly computed using localization techniques for holomorphic maps with involution. Our results are in precise agreement with mirror symmetry and large N duality predictions.Comment: 25 pages, 10 figures, published version; v4: typos correcte

New Symmetries of Supersymmetric Effective Lagrangians

We consider the structure of effective lagrangians describing the low-energy dynamics of supersymmetric theories in which a global symmetry $G$ is spontaneously broken to a subgroup $H$ while supersymmetry is unbroken. In accordance with the supersymmetric Goldstone theorem, these lagrangians contain Nambu--Goldstone superfields associated with a coset space $G^c / \hat{H}$, where $G^c$ is the complexification of $G$ and $\hat{H}$ is the largest subgroup of $G^c$ that leaves the order parameter invariant. The lagrangian may also contain additional light matter fields. To analyze the effective lagrangian for the matter fields, we first consider the case where the effective lagrangian is obtained by integrating out heavy modes at weak coupling (but including non-perturbative effects such as instantons). We show that the superpotential of the matter fields is $\hat{H}$ invariant, which can give rise to non-trivial relations among independent $H$-invariants in the superpotential. We also show that the Kahler potential of the matter fields can be restricted by a remnant of $\hat{H}$ symmetry. These results are non-perturbative and have a simple group-theoretic interpretation. When we relax the weak-coupling constraint, there appear to be additional possibilities for the action of $\hat{H}$ on the matter fields, hinting that the constraints imposed by $\hat{H}$ may be even richer in strongly coupled theories.Comment: 23 pages, plain Te

Non-compact Mirror Bundles and (0,2) Liouville Theories

We study (0,2) deformations of N=2 Liouville field theory and its mirror duality. A gauged linear sigma model construction of the ultraviolet theory connects (0,2) deformations of Liouville field theory and (0,2) deformations of N=2 SL(2,R)/U(1) coset model as a mirror duality. Our duality proposal from the gauged linear sigma model completely agrees with the exact CFT analysis. In the context of heterotic string compactifications, the deformation corresponds to the introduction of a non-trivial gauge bundle. This non-compact Landau-Ginzburg construction yields a novel way to study the gauge bundle moduli for non-compact Calabi-Yau manifolds.Comment: 34 page

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

Integrability of the N=2 boundary sine-Gordon model

We construct a boundary Lagrangian for the N=2 supersymmetric sine-Gordon model which preserves (B-type) supersymmetry and integrability to all orders in the bulk coupling constant g. The supersymmetry constraint is expressed in terms of matrix factorisations.Comment: LaTeX, 19 pages, no figures; v2: title changed, minor improvements, refs added, to appear in J. Phys. A: Math. Ge