1,342 research outputs found
Whitham Deformations of Seiberg-Witten Curves for Classical Gauge Groups
Gorsky et al. presented an explicit construction of Whitham deformations of
the Seiberg-Witten curve for the \calN = 2 SUSY Yang-Mills theory.
We extend their result to all classical gauge groups and some other cases such
as the spectral curve of the affine Toda Toda system. Our
construction, too, uses fractional powers of the superpotential that
characterizes the curve. We also consider the -plane integral of
topologically twisted theories on four-dimensional manifolds with
in the language of these explicitly constructed Whitham
deformations and an integrable hierarchy of the KdV type hidden behind.Comment: latex, 39pp, no figure; some more comments and references on
integrable systems are added, and many typos are correcte
Integrable hierarchy underlying topological Landau-Ginzburg models of D-type
A universal integrable hierarchy underlying topological Landau-Ginzburg
models of D-tye is presented. Like the dispersionless Toda hierarchy, the new
hierarchy has two distinct (``positive" and ``negative") set of flows. Special
solutions corresponding to topological Landau-Ginzburg models of D-type are
characterized by a Riemann-Hilbert problem, which can be converted into a
generalized hodograph transformation. This construction gives an embedding of
the finite dimensional small phase space of these models into the full space of
flows of this hierarchy. One of flat coordinates in the small phase space turns
out to be identical to the first ``negative" time variable of the hierarchy,
whereas the others belong to the ``positive" flows.Comment: 14 pages, Kyoto University KUCP-0061/9
DMRG and periodic boundary conditions: a quantum information perspective
We introduce a picture to analyze the density matrix renormalization group
(DMRG) numerical method from a quantum information perspective. This leads us
to introduce some modifications for problems with periodic boundary conditions
in which the results are dramatically improved. The picture also explains some
features of the method in terms of entanglement and teleportation.Comment: 4 page
Kernel Formula Approach to the Universal Whitham Hierarchy
We derive the dispersionless Hirota equations of the universal Whitham
hierarchy from the kernel formula approach proposed by Carroll and Kodama.
Besides, we also verify the associativity equations in this hierarchy from the
dispersionless Hirota equations and give a realization of the associative
algebra with structure constants expressed in terms of the residue formulas.Comment: 18 page
Critical Point of a Symmetric Vertex Model
We study a symmetric vertex model, that allows 10 vertex configurations, by
use of the corner transfer matrix renormalization group (CTMRG), a variant of
DMRG. The model has a critical point that belongs to the Ising universality
class.Comment: 2 pages, 6 figures, short not
Volume preserving multidimensional integrable systems and Nambu--Poisson geometry
In this paper we study generalized classes of volume preserving
multidimensional integrable systems via Nambu--Poisson mechanics. These
integrable systems belong to the same class of dispersionless KP type equation.
Hence they bear a close resemblance to the self dual Einstein equation. All
these dispersionless KP and dToda type equations can be studied via twistor
geometry, by using the method of Gindikin's pencil of two forms. Following this
approach we study the twistor construction of our volume preserving systems
hbar-Dependent KP hierarchy
This is a summary of a recursive construction of solutions of the
hbar-dependent KP hierarchy. We give recursion relations for the coefficients
X_n of an hbar-expansion of the operator X = X_0 + \hbar X_1 + \hbar^2 X_2 +
... for which the dressing operator W is expressed in the exponential form W =
\exp(X/\hbar). The asymptotic behaviours of (the logarithm of) the wave
function and the tau function are also considered.Comment: 12 pages, contribution to the Proceedings of the "International
Workshop on Classical and Quantum Integrable Systems 2011" (January 24-27,
2011 Protvino, Russia
SDiff(2) Toda equation -- hierarchy, function, and symmetries
A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda
equation, is shown to have a Lax formalism and an infinite hierarchy of higher
flows. The Lax formalism is very similar to the case of the self-dual vacuum
Einstein equation and its hyper-K\"ahler version, however now based upon a
symplectic structure and the group SDiff(2) of area preserving diffeomorphisms
on a cylinder . An analogue of the Toda lattice tau function is
introduced. The existence of hidden SDiff(2) symmetries are derived from a
Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function
turn out to have commutator anomalies, hence give a representation of a central
extension of the SDiff(2) algebra.Comment: 16 pages (``vanilla.sty" is attatched to the end of this file after
``\bye" command
Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method
The quasi-classical limit of the scalar nonlocal dbar-problem is derived and
a quasi-classical version of the dbar-dressing method is presented.
Dispersionless KP, mKP and 2DTL hierarchies are discussed as illustrative
examples. It is shown that the universal Whitham hierarchy it is nothing but
the ring of symmetries for the quasi-classical dbar-problem. The reduction
problem is discussed and, in particular, the d2DTL equation of B type is
derived.Comment: LaTex file,19 page
Quasi-classical limit of BKP hierarchy and W-infinity symmeties
Previous results on quasi-classical limit of the KP and Toda hierarchies are
now extended to the BKP hierarchy. Basic tools such as the Lax representation,
the Baker-Akhiezer function and the tau function are reformulated so as to fit
into the analysis of quasi-classical limit. Two subalgebras \WB_{1+\infty}
and \wB_{1+\infty} of the W-infinity algebras and
are introduced as fundamental Lie algebras of the BKP hierarchy
and its quasi-classical limit, the dispersionless BKP hierarchy. The quantum
W-infinity algebra \WB_{1+\infty} emerges in symmetries of the BKP hierarchy.
In quasi-classical limit, these \WB_{1+\infty} symmetries are shown to be
contracted into \wB_{1+\infty} symmetries of the dispersionless BKP
hierarchy.Comment: 12 pages, Kyoto University KUCP-0058/9
- …