SIM(2) and supergraphs

We construct Feynman rules and Supergraphs in SIM(2) superspace. To test our methods we perform a one-loop calculation of the effective action of the SIM(2) supersymmetric Wess-Zumino model including a term which explicitly breaks Lorentz invariance. The renormalization of the model is also discussed.Comment: 28 page

On modular spaces of semisimple Drinfeld doubles

We construct modular spaces of all 6-dimensional real semisimple Drinfeld doubles, i.e. the sets of all possible decompositions of the Lie algebra of the Drinfeld double into Manin triples. These modular spaces are significantly different from the known one for Abelian Drinfeld double, since some of these Drinfeld doubles allow decomposition into several non-isomorphic Manin triples and their modular spaces are therefore written as unions of homogeneous spaces of different dimension. Implications for Poisson-Lie T-duality and especially Poisson-Lie T-plurality are mentioned.Comment: 15 pages; introduction enlarged, added reference

Solitons and Quasielectrons in the Quantum Hall Matrix Model

We show how to incorporate fractionally charged quasielectrons in the finite quantum Hall matrix model.The quasielectrons emerge as combinations of BPS solitons and quasiholes in a finite matrix version of the noncommutative $\phi^4$ theory coupled to a noncommutative Chern-Simons gauge field. We also discuss how to properly define the charge density in the classical matrix model, and calculate density profiles for droplets, quasiholes and quasielectrons.Comment: 15 pages, 9 figure

Worldsheet boundary conditions in Poisson-Lie T-duality

We apply canonical Poisson-Lie T-duality transformations to bosonic open string worldsheet boundary conditions, showing that the form of these conditions is invariant at the classical level, and therefore they are compatible with Poisson-Lie T-duality. In particular the conditions for conformal invariance are automatically preserved, rendering also the dual model conformal. The boundary conditions are defined in terms of a gluing matrix which encodes the properties of D-branes, and we derive the duality map for this matrix. We demonstrate explicitly the implications of this map for D-branes in two non-Abelian Drinfel'd doubles.Comment: 20 pages, Latex; v2: typos and wording corrected, references added; v3: three-dimensional example added, reference added, discussion clarified, published versio

Quantum equivalence in Poisson-Lie T-duality

We prove that, general \s-models related by Poisson-Lie T-duality are quantum equivalent under one-loop renormalization group flow. We reveal general properties of the flows, we study the associated generalized coset models and provide explicit examples.Comment: 16 page

Generalized Kahler manifolds and off-shell supersymmetry

We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kahler potential for any generalized Kahler manifold; this potential is the superspace Lagrangian.Comment: 21 pages; references clarified and added; theorem generalized; typos correcte

Topological twisted sigma model with H-flux revisited

In this paper we revisit the topological twisted sigma model with H-flux. We explicitly expand and then twist the worldsheet Lagrangian for bi-Hermitian geometry. we show that the resulting action consists of a BRST exact term and pullback terms, which only depend on one of the two generalized complex structures and the B-field. We then discuss the topological feature of the model.Comment: 16 pages. Appendix adde

Brane Boxes: Bending and Beta Functions

We study the type IIB brane box configurations recently introduced by Hanany and Zaffaroni. We show that even at finite string coupling, one can construct smooth configurations of branes with fairly arbitrary gauge and flavor structure. Limiting our attention to the better understood case where NS-branes do not intersect over a four dimensional surface gives some restrictions on the theories, but still permits many examples, both anomalous and non-anomalous. We give several explicit examples of such configurations and discuss what constraints can be imposed on brane-box theories from bending considerations. We also discuss the relation between brane bending and beta-functions for brane-box configurations.Comment: latex, 18 pages, 8 figure