10 research outputs found
Supersymmetry Flows, Semi-Symmetric Space Sine-Gordon Models And The Pohlmeyer Reduction
We study the extended supersymmetric integrable hierarchy underlying the
Pohlmeyer reduction of superstring sigma models on semi-symmetric superspaces
F/G. This integrable hierarchy is constructed by coupling two copies of the
homogeneous integrable hierarchy associated to the loop Lie superalgebra
extension f of the Lie superalgebra f of F and this is done by means of the
algebraic dressing technique and a Riemann-Hilbert factorization problem. By
using the Drinfeld-Sokolov procedure we construct explicitly, a set of 2D spin
\pm1/2 conserved supercharges generating supersymmetry flows in the phase space
of the reduced model. We introduce the bi-Hamiltonian structure of the extended
homogeneous hierarchy and show that the two brackets are of the
Kostant-Kirillov type on the co-adjoint orbits defined by the light-cone Lax
operators L_\pm. By using the second symplectic structure, we show that these
supersymmetries are Hamiltonian flows, we compute part of the supercharge
algebra and find the supersymmetric field variations they induce. We also show
that this second Poisson structure coincides with the canonical
Lorentz-Invariant symplectic structure of the WZNW model involved in the
Lagrangian formulation of the extended integrable hierarchy, namely, the
semi-symmetric space sine-Gordon model (SSSSG), which is the Pohlmeyer reduced
action functional for the transverse degrees of freedom of superstring sigma
models on the cosets F/G. We work out in some detail the Pohlmeyer reduction of
the AdS_2xS^2 and the AdS_3xS^3 superstrings and show that the new conserved
supercharges can be related to the supercharges extracted from 2D superspace.
In particular, for the AdS_2xS^2 example, they are formally the same.Comment: V2: Two references added, V3: Modifications in section 2.6, V4:
Published versio
Nonlinear Super Integrable Couplings of Super Classical-Boussinesq Hierarchy
Nonlinear integrable couplings of super classical-Boussinesq hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then, its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of the classical integrable hierarchy were obtained
Super-Hamiltonian Structures and Conservation Laws of a New Six-Component Super-Ablowitz-Kaup-Newell-Segur Hierarchy
A six-component super-Ablowitz-Kaup-Newell-Segur (-AKNS) hierarchy is proposed by the zero curvature equation associated with Lie superalgebras. Supertrace identity is used to furnish the super-Hamiltonian structures for the resulting nonlinear superintegrable hierarchy. Furthermore, we derive the infinite conservation laws of the first two nonlinear super-AKNS equations in the hierarchy by utilizing spectral parameter expansions. PACS: 02.30.Ik; 02.30.Jr; 02.20.Sv
Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
Nonlinear SUSY approach to preparation of quantum systems with pre-planned
spectral properties is reviewed. Possible multidimensional extensions of
Nonlinear SUSY are described. The full classification of ladder-reducible and
irreducible chains of SUSY algebras in one-dimensional QM is given. Emergence
of hidden symmetries and spectrum generating algebras is elucidated in the
context of Nonlinear SUSY in one- and two-dimensional QM.Comment: 75 pages, Minor corrections, Version published in Journal of Physics
T-systems and Y-systems in integrable systems
The T and Y-systems are ubiquitous structures in classical and quantum
integrable systems. They are difference equations having a variety of aspects
related to commuting transfer matrices in solvable lattice models, q-characters
of Kirillov-Reshetikhin modules of quantum affine algebras, cluster algebras
with coefficients, periodicity conjectures of Zamolodchikov and others,
dilogarithm identities in conformal field theory, difference analogue of
L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem,
AdS/CFT correspondence, Toda field equations on discrete space-time, Laplace
sequence in discrete geometry, Fermionic character formulas and combinatorial
completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics,
analytic and thermodynamic Bethe ans\"atze, quantum transfer matrix method and
so forth. This review article is a collection of short reviews on these topics
which can be read more or less independently.Comment: 156 pages. Minor corrections including the last paragraph of sec.3.5,
eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical
review) also needs these correction