383 research outputs found
Backlund Transformations, D-Branes, and Fluxes in Minimal Type 0 Strings
We study the Type 0A string theory in the (2,4k) superconformal minimal model
backgrounds, focusing on the fully non-perturbative string equations which
define the partition function of the model. The equations admit a parameter,
Gamma, which in the spacetime interpretation controls the number of background
D-branes, or R-R flux units, depending upon which weak coupling regime is
taken. We study the properties of the string equations (often focusing on the
(2,4) model in particular) and their physical solutions. The solutions are the
potential for an associated Schrodinger problem whose wavefunction is that of
an extended D-brane probe. We perform a numerical study of the spectrum of this
system for varying Gamma and establish that when Gamma is a positive integer
the equations' solutions have special properties consistent with the spacetime
interpretation. We also show that a natural solution-generating transformation
(that changes Gamma by an integer) is the Backlund transformation of the KdV
hierarchy specialized to (scale invariant) solitons at zero velocity. Our
results suggest that the localized D-branes of the minimal string theories are
directly related to the solitons of the KdV hierarchy. Further, we observe an
interesting transition when Gamma=-1.Comment: 17 pages, 3 figure
Generalized Tu Formula and Hamilton Structures of Fractional Soliton Equation Hierarchy
With the modified Riemann-Liouville fractional derivative, a fractional Tu
formula is presented to investigate generalized Hamilton structure of
fractional soliton equations. The obtained results can be reduced to the
classical Hamilton hierachy of ordinary calculus.Comment: 12 p
A generalized fractional KN equation hierarchy and its fractional Hamiltonian structure
AbstractA generalized Hamiltonian structure of the fractional soliton equation hierarchy is presented by using differential forms and exterior derivatives of fractional orders. We construct the generalized fractional trace identity through the Riemann–Liouville fractional derivative. An example of the fractional KN soliton equation hierarchy and Hamiltonian structure is presented, which is a new integrable hierarchy and possesses Hamiltonian structure
Constrained KP Hierarchies: Additional Symmetries, Darboux-B\"{a}cklund Solutions and Relations to Multi-Matrix Models
This paper provides a systematic description of the interplay between a
specific class of reductions denoted as \cKPrm () of the primary
continuum integrable system -- the Kadomtsev-Petviashvili ({\sf KP}) hierarchy
and discrete multi-matrix models. The relevant integrable \cKPrm structure is a
generalization of the familiar -reduction of the full {\sf KP} hierarchy to
the generalized KdV hierarchy . The important feature
of \cKPrm hierarchies is the presence of a discrete symmetry structure
generated by successive Darboux-B\"{a}cklund (DB) transformations. This
symmetry allows for expressing the relevant tau-functions as Wronskians within
a formalism which realizes the tau-functions as DB orbits of simple initial
solutions. In particular, it is shown that any DB orbit of a
defines a generalized 2-dimensional Toda lattice structure. Furthermore, we
consider the class of truncated {\sf KP} hierarchies ({\sl i.e.}, those defined
via Wilson-Sato dressing operator with a finite truncated pseudo-differential
series) and establish explicitly their close relationship with DB orbits of
\cKPrm hierarchies. This construction is relevant for finding partition
functions of the discrete multi-matrix models.
The next important step involves the reformulation of the familiar
non-isospectral additional symmetries of the full {\sf KP} hierarchy so that
their action on \cKPrm hierarchies becomes consistent with the constraints of
the reduction. Moreover, we show that the correct modified additional
symmetries are compatible with the discrete DB symmetry on the \cKPrm DB
orbits.
The above technical arsenal is subsequently applied to obtain completeComment: LaTeX, 63 pg
Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
We review various connections between condensed matter systems with the
Nambu-Jona Lasinio model and nonlinear sigma models. The field theoretical
description of interacting systems offers a systematic framework to describe
the dynamical generation of condensates. Resent findings of a duality between
the Nambu-Jona Lasinio model and the nonlinear sigma model enables us to
investigate various properties underlying both theories. In this review we
mainly focus on inhomogeneous condensations in static situations. The various
methods developed in the Nambu-Jona Lasinio model reveal the inhomogeneous
phase structures and also yield new inhomogeneous solutions in the nonlinear
sigma model owing to the duality. The recent progress on interacting systems in
finite systems is also reviewed.Comment: 24pages, 10 figures, Invited review paper commissioned by Symmetry.
Comments warmly welcom
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