N = 2 world-sheet approach to D-branes on generalized Kaehler geometries: I. General formalism

We present an N = 2 world-sheet superspace description of D-branes on bihermitian or generalized Kaehler manifolds. To accomplish this, D-branes are considered as boundary conditions for a nonlinear sigma-model in what we call N = 2 boundary superspace. In this note the general formalism for such an approach is presented and the resulting classification sketched. This includes some remarks regarding target spaces whose parameterization includes semi-chiral superfields which have not appeared in the literature yet. In an accompanying note we turn to some examples and applications of the general setup presented here.Comment: 7 pages, contribution to the proceedings of the Fourth Workshop of the RTN project 'Constituents, Fundamental Forces and Symmetries of the Universe', Varna, September 11 - 17, 200

Extensions of 2D Gravity

After reviewing some aspects of gravity in two dimensions, it is shown that non-trivial embeddings of sl(2) in a semi-simple (super) Lie algebra give rise to a very large class of extensions of 2D gravity. The induced action is constructed as a gauged WZW model and an exact expression for the effective action is given. (Talk presented at the Journees Relativistes '93, Brussels, April, 1993).Comment: 12 pages (LaTeX, 3 eps figures), LBL-34240, UCB-PTH-93/2

Strings, gravity and particle physics

This contribution, aimed mostly at experimental particle physicists, reviews some of the main ideas and results of String Theory in a non-technical language. It originates from the talks presented by the authors at the Electro-Weak session of the 2002 Moriond Meeting, here merged in an attempt to provide a more complete and concise view of the subject.Comment: LaTeX, 28 pages, 13 figures. Contribution to the proceedings of the 2002 Rencontres de Moriond "Electroweak interactions and unified theories

Quantum gauging from classical gauging of nonlinear algebras

We extend the theory of the gauging of classical quadratically nonlinear algebras without a central charge but with a coset structure, to the quantum level. Inserting the minimal anomalies into the classical transformation rules of the currents introduces further quantum corrections to the classical transformation rules of the gauge fields and currents which additively renormalize the structure constants. The corresponding Ward identities are the c -> infinity limit of the full quantum Ward identities, and reveal that the c -> infinity limit of the quantum gauge algebra closes on fields and currents. Two examples are given.Comment: 16 pages, LaTeX, ITP-SB-92-67, LBL-33339, UCB-PTH-92/4

An N=2 worldsheet approach to D-branes in bihermitian geometries: I. Chiral and twisted chiral fields

We investigate N=(2,2) supersymmetric nonlinear sigma-models in the presence of a boundary. We restrict our attention to the case where the bulk geometry is described by chiral and twisted chiral superfields corresponding to a bihermitian bulk geometry with two commuting complex structures. The D-brane configurations preserving an N=2 worldsheet supersymmetry are identified. Duality transformations interchanging chiral for twisted chiral fields and vice versa while preserving all supersymmetries are explicitly constructed. We illustrate our results with various explicit examples such as the WZW-model on the Hopf surface S3xS1. The duality transformations provide e.g new examples of coisotropic A-branes on Kahler manifolds (which are not necessarily hyper-Kahler). Finally, by dualizing a chiral and a twisted chiral field to a semi-chiral multiplet, we initiate the study of D-branes in bihermitian geometries where the cokernel of the commutator of the complex structures is non-empty.Comment: LaTeX, 50 page

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

Superstrings from Hamiltonian Reduction

In any string theory there is a hidden, twisted superconformal symmetry algebra, part of which is made up by the BRST current and the anti-ghost. We investigate how this algebra can be systematically constructed for strings with $N\!-\!2$ supersymmetries, via quantum Hamiltonian reduction of the Lie superalgebras $osp(N|2)$. The motivation is to understand how one could systematically construct generalized string theories from superalgebras. We also briefly discuss the BRST algebra of the topological string, which is a doubly twisted $N\!=\!4$ superconformal algebra.Comment: 32p, LaTeX, CERN-TH.7379/9

Coset Construction and Character Sumrules for the Doubly Extended N=4N=4 Superconformal Algebras

Character sumrules associated with the realization of the $N=4$ superconformal algebra \At on manifolds corresponding to the group cosets SU(3)_{\ktp }/U(1) are derived and developed as an important tool in obtaining the modular properties of \At characters as well as information on certain extensions of that algebra. Their structure strongly suggests the existence of rational conformal field theories with central charges in the range $1 \le c\le 4$. The corresponding characters appear in the massive sector of the sumrules and are completely specified in terms of the characters for the parafermionic theory $SU(3)/(SU(2)\times U(1))$ and in terms of the branching functions of massless \At characters into SU(2)_{\ktp }\times SU(2)_1 characters.Comment: 31 pages, DTP/92/49 NBI-HE-92-73 (latex file