Reduction of Courant algebroids and generalized complex structures

We present a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized K\"ahler structures which interpolates between holomorphic reduction of complex manifolds and symplectic reduction. The enhanced symmetry group of a Courant algebroid leads us to define \emph{extended} actions and a generalized notion of moment map. Key examples of generalized K\"ahler reduced spaces include new explicit bi-Hermitian metrics on \CC P^2.Comment: 34 pages. Presentation greatly improved, one subsection added, errors corrected, references added. v3: a few changes in the presentation, material slightly reorganized, final version to appear in Adv. in Mat

Free Field Realization of N=2N=2 Super W3W_{3} Algebra

We study the quantum $N=2$ super-$W_{3}$ algebra using the free field realization, which is obtained from the supersymmetric Miura transformation associated with the Lie superalgebra $A(2|1)$. We compute the full operator product expansions of the algebra explicitly. It is found that the results agree with those obtained by the OPE method.Comment: 10 pages, latex, NBI-HE-93-0

CFT Description of String Theory Compactified on Non-compact Manifolds with G_2 Holonomy

We construct modular invariant partition functions for strings propagating on non-compact manifolds of G_2 holonomy. Our amplitudes involve a pair of N=1 minimal models M_m, M_{m+2} (m=3,4,...) and are identified as describing strings on manifolds of G_2 holonomy associated with A_{m-2} type singularity. It turns out that due to theta function identities our amplitudes may be cast into a form which contain tricritical Ising model for any m. This is in accord with the results of Shatashvili and Vafa. We also construct a candidate partition function for string compactified on a non-compact Spin(7) manifold.Comment: It is found that tricritical Ising model is contained in our amplitues in agreement with the results of Shatashvili and Vafa. Manuscript is revised accordingly. A new reference is also adde

A New Deformation of W-Infinity and Applications to the Two-loop WZNW and Conformal Affine Toda Models

We construct a centerless W-infinity type of algebra in terms of a generator of a centerless Virasoro algebra and an abelian spin-1 current. This algebra conventionally emerges in the study of pseudo-differential operators on a circle or alternatively within KP hierarchy with Watanabe's bracket. Construction used here is based on a special deformation of the algebra $w_{\infty}$ of area preserving diffeomorphisms of a 2-manifold. We show that this deformation technique applies to the two-loop WZNW and conformal affine Toda models, establishing henceforth $W_{\infty}$ invariance of these models.Comment: 8 page

String Theory on G_2 Manifolds Based on Gepner Construction

We study the type II string theories compactified on manifolds of $G_2$ holonomy of the type ({Calabi-Yau 3-fold} \times S^1)/\bz_2 where $CY_3$ sectors realized by the Gepner models. We construct modular invariant partition functions for $G_2$ manifold for arbitrary Gepner models of the Calabi-Yau sector. We note that the conformal blocks contain the tricritical Ising model and find extra massless states in the twisted sectors of the theory when all the levels $k_i$ of minimal models in Gepner constructions are even.Comment: 20 pages, no figure, improvement on some technical points in the discussions of twisted sector

Darboux Transformations for Supersymmetric Korteweg - de Vries Equations

\hspace{.2in}We consider the Darboux type transformations for the spectral problems of supersymmetric KdV systems. The supersymmetric analogies of Darboux and Darboux-Levi transformations are established for the spectral problems of Manin-Radul-Mathieu sKdV and Manin-Radul sKdV. Several B\"acklund transformations are derived for the MRM sKdV and MR sKdV systems.Comment: Latex, 8 pages AS-ITP-94-4

Odd Hamiltonian Structure for Supersymmetric Sawada - Kotera Equation

We study the supersymmetric N=1 hierarchy connected with the Lax operator of the supersymmetric Sawada-Kotera equation. This operator produces the physical equations as well as the exotic equations with odd time. The odd Bi-Hamiltonian structure for the N=1 Supersymmetric Sawada - Kotera equation is defined. The product of the symplectic and implectic Hamiltonian operator gives us the recursion operator. In that way we prove the integrability of the supersymmetric Sawada - Kotera equation in the sense that it has the Bi-Hamiltonian structure. The so called "quadratic" Hamiltonian operator of even order generates the exotic equations while the "cubic" odd Hamiltonian operator generates the physical equations.Comment: 11 pages, several nisprints are corrected, text is modified, Will appear in Phys.Lett