Deformed fields and Moyal construction of deformed super Virasoro algebra

Studied is the deformation of super Virasoro algebra proposed by Belov and Chaltikhian. Starting from abstract realizations in terms of the FFZ type generators, various connections of them to other realizations are shown, especially to deformed field representations, whose bosonic part generator is recently reported as a deformed string theory on a noncommutative world-sheet. The deformed Virasoro generators can also be expressed in terms of ordinary free fields in a highly nontrivial way.Comment: neutral fields are replaced by complex fields almost everywhere in Sects. 6 and

Discrete and Continuous Bogomolny Equations through the Deformed Algebra

We connect the discrete and continuous Bogomolny equations. There exists one-parameter algebra relating two equations which is the deformation of the extended conformal algebra. This shows that the deformed algebra plays the role of the link between the matrix valued model and the model with one more space dimension higher.Comment: 12 page

Deformation of Super Virasoro Algebra in Noncommutative Quantum Superspace

We present a twisted commutator deformation for $N=1,2$ super Virasoro algebras based on $GL_q(1,1)$ covariant noncommutative superspace.Comment: 10 pages, Late

Discretization of Virasoro Algebra

A $q$-discretization of \vi\ algebra is studied which reduces to the ordinary \vi\ algebra in the limit of q \ra 1. This is derived starting from the Moyal bracket algebra, hence is a kind of quantum deformation different from the quantum groups. Representation of this new algebra by using $q$-parametrized free fields is also given.Comment: 12 pages, Latex, TMUP-HEL-930

The dispersive self-dual Einstein equations and the Toda lattice

The Boyer-Finley equation, or $SU(\infty)$-Toda equation is both a reduction of the self-dual Einstein equations and the dispersionlesslimit of the $2d$-Toda lattice equation. This suggests that there should be a dispersive version of the self-dual Einstein equation which both contains the Toda lattice equation and whose dispersionless limit is the familiar self-dual Einstein equation. Such a system is studied in this paper. The results are achieved by using a deformation, based on an associative $\star$-product, of the algebra $sdiff(\Sigma^2)$ used in the study of the undeformed, or dispersionless, equations.Comment: 11 pages, LaTeX. To appear: J. Phys.

D=5 Simple Supergravity on AdS_2 \times S^3

The Kaluza-Klein spectrum of D=5 simple supergravity compactified on S^3 is studied. A classical background solution which preserves maximal supersymmetry is fulfilled by the geometry of AdS_2\times S^3. The physical spectrum of the fluctuations is classified according to SU(1,1|2)\times SU(2) symmetry, which has a very similar structure to that in the case of compactification on AdS_3\times S^2.Comment: 14 pages, Latex, 4 figures; some description improve

Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems

Inspired by the fact that the Moyal quantization is related with nonlocal operation, I define a difference analogue of vector fields and rephrase quantum description on the phase space. Applying this prescription to the theory of the KP-hierarchy, I show that their integrability follows to the nature of their Wigner distribution. Furthermore the definition of the ``expectation value'' clarifies the relation between our approach and the Hamiltonian structure of the KP-hierarchy. A trial of the explicit construction of the Moyal bracket structure in the integrable system is also made.Comment: 19 pages, to appear in J. Phys. Soc. Jp