Scattering of Noncommutative Waves and Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions

Interactions of noncommutative waves and solitons in 2+1 dimensions can be analyzed exactly for a supersymmetric and integrable U(n) chiral model extending the Ward model. Using the Moyal-deformed dressing method in an antichiral superspace, we construct explicit time-dependent solutions of its noncommutative field equations by iteratively solving linear equations. The approach is illustrated by presenting scattering configurations for two noncommutative U(2) plane waves and for two noncommutative U(2) solitons as well as by producing a noncommutative U(1) two-soliton bound state.Comment: 1+13 pages; v2: reference added, version published in JHE

The sl(2n|2n)^(1) Super-Toda Lattices and the Heavenly Equations as Continuum Limit

The $n\to\infty$ continuum limit of super-Toda models associated with the affine $sl(2n|2n)^{(1)}$ (super)algebra series produces $(2+1)$-dimensional integrable equations in the ${\bf S}^{1}\times {\bf R}^2$ spacetimes. The equations of motion of the (super)Toda hierarchies depend not only on the chosen (super)algebras but also on the specific presentation of their Cartan matrices. Four distinct series of integrable hierarchies in relation with symmetric-versus-antisymmetric, null-versus-nonnull presentations of the corresponding Cartan matrices are investigated. In the continuum limit we derive four classes of integrable equations of heavenly type, generalizing the results previously obtained in the literature. The systems are manifestly N=1 supersymmetric and, for specific choices of the Cartan matrix preserving the complex structure, admit a hidden N=2 supersymmetry. The coset reduction of the (super)-heavenly equation to the ${\bf I}\times{\bf R}^{(2)}=({\bf S}^{1}/{\bf Z}_2)\times {\bf R}^2$ spacetime (with ${\bf I}$ a line segment) is illustrated. Finally, integrable $N=2,4$ supersymmetrically extended models in $(1+1)$ dimensions are constructed through dimensional reduction of the previous systems.Comment: 12 page

Solitons of Sigma Model on Noncommutative Space as Solitons of Electron System

We study the relationship of soliton solutions for electron system with those of the sigma model on the noncommutative space, working directly in the operator formalism. We find that some soliton solutions of the sigma model are also the solitons of the electron system and are classified by the same topological numbers.Comment: 12 pages, LaTeX2e, improvements to discussions, Version to be published in JHE

Transmogrifying Fuzzy Vortices

We show that the construction of vortex solitons of the noncommutative Abelian-Higgs model can be extended to a critically coupled gauged linear sigma model with Fayet-Illiopolous D-terms. Like its commutative counterpart, this fuzzy linear sigma model has a rich spectrum of BPS solutions. We offer an explicit construction of the degree$-k$ static semilocal vortex and study in some detail the infinite coupling limit in which it descends to a degree$-k$ \C\Pk^{N} instanton. This relation between the fuzzy vortex and noncommutative lump is used to suggest an interpretation of the noncommutative sigma model soliton as tilted D-strings stretched between an NS5-brane and a stack of D3-branes in type IIB superstring theory.Comment: 21 pages, 4 figures, LaTeX(JHEP3

Matrix Models and D-branes in Twistor String Theory

We construct two matrix models from twistor string theory: one by dimensional reduction onto a rational curve and another one by introducing noncommutative coordinates on the fibres of the supertwistor space P^(3|4)->CP^1. We comment on the interpretation of our matrix models in terms of topological D-branes and relate them to a recently proposed string field theory. By extending one of the models, we can carry over all the ingredients of the super ADHM construction to a D-brane configuration in the supertwistor space P^(3|4). Eventually, we present the analogue picture for the (super) Nahm construction.Comment: 1+37 pages, reference added, JHEP style, published versio

Lost equivalence of nonlinear sigma and CP1CP^{1} models on noncommutative space

We show that the equivalence of nonlinear sigma and $CP^{1}$ models which is valid on the commutative space is broken on the noncommutative space. This conclusion is arrived at through investigation of new BPS solitons that do not exist in the commutative limit.Comment: 17 pages, LaTeX2

On the N=2 Supersymmetric Camassa-Holm and Hunter-Saxton Equations

We consider N=2 supersymmetric extensions of the Camassa-Holm and Hunter-Saxton equations. We show that they admit geometric interpretations as Euler equations on the superconformal algebra of contact vector fields on the 1|2-dimensional supercircle. We use the bi-Hamiltonian formulation to derive Lax pairs. Moreover, we present some simple examples of explicit solutions. As a by-product of our analysis we obtain a description of the bounded traveling-wave solutions for the two-component Hunter-Saxton equation.Comment: 1+19 pages, 3 figures; v2: reference added; v3: more references added, published in LM

Higher Loop Spin Field Correlators in D=4 Superstring Theory

We develop calculational tools to determine higher loop superstring correlators involving massless fermionic and spin fields in four space time dimensions. These correlation functions are basic ingredients for the calculation of loop amplitudes involving both bosons and fermions in D=4 heterotic and superstring theories. To obtain the full amplitudes in Lorentz covariant form the loop correlators of fermionic and spin fields have to be expressed in terms of SO(1,3) tensors. This is one of the main achievements in this work.Comment: 59 pages, 1 figure; v2: final version published in JHE

Vacuum Energy Cancellation in a Non-supersymmetric String

We present a nonsupersymmetric orbifold of type II string theory and show that it has vanishing cosmological constant at the one and two loop level. We argue heuristically that the cancellation persists at higher loops.Comment: 31 pages harvmac big, 6 figures. New version includes the 2-loop analysis of hep-th/9810129 and elimination of one of the two heuristic arguments for higher loop cancellatio