2,188 research outputs found
Quantum and Classical Aspects of Deformed Strings.
The quantum and classical aspects of a deformed matrix model proposed
by Jevicki and Yoneya are studied. String equations are formulated in the
framework of Toda lattice hierarchy. The Whittaker functions now play the role
of generalized Airy functions in strings. This matrix model has two
distinct parameters. Identification of the string coupling constant is thereby
not unique, and leads to several different perturbative interpretations of this
model as a string theory. Two such possible interpretations are examined. In
both cases, the classical limit of the string equations, which turns out to
give a formal solution of Polchinski's scattering equations, shows that the
classical scattering amplitudes of massless tachyons are insensitive to
deformations of the parameters in the matrix model.Comment: 52 pages, Latex
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
Toda Lattice Hierarchy and Generalized String Equations
String equations of the -th generalized Kontsevich model and the
compactified string theory are re-examined in the language of the Toda
lattice hierarchy. As opposed to a hypothesis postulated in the literature, the
generalized Kontsevich model at does not coincide with the
string theory at self-dual radius. A broader family of solutions of the Toda
lattice hierarchy including these models are constructed, and shown to satisfy
generalized string equations. The status of a variety of string
models is discussed in this new framework.Comment: 35pages, LaTeX Errors are corrected in Eqs. (2.21), (2.36), (2.33),
(3.3), (5.10), (6.1), sentences after (3.19) and theorem 5. A few references
are update
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
Unknotting numbers and triple point cancelling numbers of torus-covering knots
It is known that any surface knot can be transformed to an unknotted surface
knot or a surface knot which has a diagram with no triple points by a finite
number of 1-handle additions. The minimum number of such 1-handles is called
the unknotting number or the triple point cancelling number, respectively. In
this paper, we give upper bounds and lower bounds of unknotting numbers and
triple point cancelling numbers of torus-covering knots, which are surface
knots in the form of coverings over the standard torus . Upper bounds are
given by using -charts on presenting torus-covering knots, and lower
bounds are given by using quandle colorings and quandle cocycle invariants.Comment: 26 pages, 14 figures, added Corollary 1.7, to appear in J. Knot
Theory Ramification
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
On a class of multidimensional integrable hierarchies and their reductions
A class of multidimensional integrable hierarchies connected with commutation
of general (unreduced) (N+1)-dimensional vector fields containing derivative
over spectral variable is considered. They are represented in the form of
generating equation, as well as in the Lax-Sato form. A dressing scheme based
on nonlinear vector Riemann problem is presented for this class. The
hierarchies connected with Manakov-Santini equation and Dunajski system are
considered as illustrative examples.Comment: Talk at NLP5 conference, Gallipoli. 8 pages. Formulae for the second
flows of Dunajski equation hierarchy corrected (page 6
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