scholarly journals Extended Toda lattice hierarchy, extended two-matrix model and c = 1 string theory

1995 ◽  
Vol 434 (1-2) ◽  
pp. 408-444 ◽  
Author(s):  
L. Bonora ◽  
C.S. Xiong
Keyword(s):  
String Theory ◽  
Matrix Model ◽  
Toda Lattice ◽  
Toda Lattice Hierarchy

scholarly journals ABJM matrix model and 2D Toda lattice hierarchy

2019 ◽  
Vol 2019 (3) ◽  
Author(s):  
Tomohiro Furukawa ◽  
Sanefumi Moriyama
Keyword(s):  
Matrix Model ◽  
Toda Lattice ◽  
Toda Lattice Hierarchy

INTEGRABLE STRUCTURES OF UNITARY MATRIX MODELS

1992 ◽  
Vol 07 (20) ◽  
pp. 4803-4824 ◽  
Author(s):  
S. KHARCHEV ◽  
A. MIRONOV
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Toda Lattice ◽  
Discrete Analog ◽  
Unitary Matrix ◽  
Component Systems ◽  
Unitary Model ◽  
Two Component Systems ◽  
Hermitian Matrix Model ◽  
Toda Lattice Hierarchy

The unitary matrix model is considered from the viewpoint of integrability. We demonstrate that this is an integrable system embedded into a two-dimensional Toda lattice hierarchy which corresponds to an integrable chain (modified Volterra) under a special reduction. The interrelations between this chain and other chains (like the Toda one) are demonstrated to be given by Bäcklund transformations. The case of the symmetric unitary model is discussed in detail and demonstrated to be connected with the Hermitian matrix model. This connection as a discrete analog of the correspondence between KdV and MKdV systems is investigated more thoroughly. We also demonstrate that unitary matrix models can be considered as two-component systems as well.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KdV HIERARCHIES AND THE TWO-MATRIX MODEL

1995 ◽  
Vol 10 (17) ◽  
pp. 2537-2577 ◽  
Author(s):  
H. ARATYN ◽  
E. NISSIMOV ◽  
S. PACHEVA ◽  
A.H. ZIMERMAN
Keyword(s):  
Poisson Bracket ◽  
Hamiltonian Structure ◽  
Toda Lattice ◽  
Free Field ◽  
String Model ◽  
Matrix Formulation ◽  
Hamiltonian Action ◽  
Kdv Hierarchy ◽  
Associated Matrix ◽  
Toda Lattice Hierarchy

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL (M+1, M−k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL (M+1, M−k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M−k) Poisson bracket algebras generalizing the familiar nonlinear WM+1 algebra. Discrete Bäcklund transformations for SL (M+1, M−k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL (M+1, 1) KdV hierarchy.

The generalized additional symmetries of the two-Toda lattice hierarchy

2013 ◽  
Vol 54 (2) ◽  
pp. 023513 ◽  
Author(s):  
Jipeng Cheng ◽  
Ye Tian ◽  
Zhaowen Yan ◽  
Jingsong He
Keyword(s):  
Toda Lattice ◽  
Additional Symmetries ◽  
Toda Lattice Hierarchy

A generalized integrable hierarchy related to the relativistic Toda lattice: Hamiltonian structure, Darboux transformation, soliton solution and conservation law

2021 ◽  
Author(s):  
Zhiguo Xu
Keyword(s):  
Darboux Transformation ◽  
Hamiltonian Structure ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Integrable Hierarchy ◽  
Integrable Lattice ◽  
Pass Through ◽  
Matrix Spectral Problem ◽  
Relativistic Toda Lattice ◽  
Toda Lattice Hierarchy

Starting from a more generalized discrete [Formula: see text] matrix spectral problem and using the Tu scheme, some integrable lattice hierarchies (ILHs) are presented which include the well-known relativistic Toda lattice hierarchy and some new three-field ILHs. Taking one of the hierarchies as example, the corresponding Hamiltonian structure is constructed and the Liouville integrability is illustrated. For the first nontrivial lattice equation in the hierarchy, the [Formula: see text]-fold Darboux transformation (DT) of the system is established basing on its Lax pair. By using the obtained DT, we generate the discrete [Formula: see text]-soliton solutions in determinant form and plot their figures with proper parameters, from which we get some interesting soliton structures such as kink and anti-bell-shaped two-soliton, kink and anti-kink-shaped two-soliton and so on. These soliton solutions are much stable during the propagation, the solitary waves pass through without change of shapes, amplitudes, wave-lengths and directions. Finally, we derive infinitely many conservation laws of the system and give the corresponding conserved density and associated flux formulaically.

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