POSSIBLE IMPLICATIONS OF INTEGRABLE SYSTEMS FOR STRING THEORY

1991 ◽  
Vol 06 (06) ◽  
pp. 977-988 ◽  
Author(s):  
A. GERASIMOV ◽  
D. LEBEDEV ◽  
A. MOROZOV
Keyword(s):  
String Theory ◽  
Lie Algebras ◽  
Spectral Parameter ◽  
Integrable Systems ◽  
Integrable Models ◽  
Lax Representation ◽  
Two Dimensional ◽  
Deformed Algebra ◽  
Area Preserving

A kind of program for the unification of conformal and two-dimensional integrable models is described. Integrable systems, defined by the condition of vanishing curvature (Lax representation), can be derived from universal generalizations of Wess-Zumino-Witten action, including one more integration (over spectral parameter λ). Such actions, in their turn, should be derivable from some membrane-like action, related to the Kirillov-Kostant form for some quantum two-loop Lie algebras (like complexification of Fairlie’s deformed algebra of two-dimensional area-preserving reparametrizations).

DEFORMATIONS OF LOOP ALGEBRAS AND CLASSICAL INTEGRABLE SYSTEMS: FINITE-DIMENSIONAL HAMILTONIAN SYSTEMS

2004 ◽  
Vol 16 (07) ◽  
pp. 823-849 ◽  
Author(s):  
T. SKRYPNYK
Keyword(s):  
Lie Algebras ◽  
Hamiltonian Systems ◽  
Spectral Parameter ◽  
Integrable Systems ◽  
Integrable Hamiltonian Systems ◽  
Infinite Dimensional ◽  
Loop Algebras ◽  
Finite Dimensional ◽  
Quasigraded Lie Algebras ◽  
Classical Integrable

We construct a family of infinite-dimensional quasigraded Lie algebras, that could be viewed as deformation of the graded loop algebras and admit Kostant–Adler scheme. Using them we obtain new integrable hamiltonian systems admitting Lax-type representations with the spectral parameter.

FROM INHOMOGENEOUS SIX-VERTEX LATTICE MODELS TO CONTINUUM QUANTUM INTEGRABLE MODELS

1992 ◽  
Vol 07 (25) ◽  
pp. 6385-6403
Author(s):  
Y.K. ZHOU
Keyword(s):  
Integrable Systems ◽  
Scaling Limit ◽  
Lattice Models ◽  
Integrable Models ◽  
Two Dimensional ◽  
Vertex Model ◽  
Quantum Integrable Systems ◽  
Vertex Models ◽  
Quantum Integrable Models ◽  
Sine Gordon Model

A method to find continuum quantum integrable systems from two-dimensional vertex models is presented. We explain the method with the example where the quantum sine-Gordon model is obtained from an inhomogeneous six-vertex model in its scaling limit. We also show that the method can be applied to other models.

scholarly journals INTERACTION OF DISCRETE STATES IN TWO-DIMENSIONAL STRING THEORY

1991 ◽  
Vol 06 (35) ◽  
pp. 3273-3281 ◽  
Author(s):  
I. R. KLEBANOV ◽  
A. M. POLYAKOV
Keyword(s):  
String Theory ◽  
Effective Action ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Discrete States ◽  
Structure Constants ◽  
Area Preserving

We study the couplings of discrete states that appear in the string theory embedded in two dimensions, and show that they are given by the structure constants of the group of area preserving diffeomorphisms. We propose an effective action for these states, which is itself invariant under this infinite-dimensional group.

scholarly journals Notes on Curtright–Zachos Deformations of osp(1,2) and Super Virasoro Algebras

1997 ◽  
Vol 12 (32) ◽  
pp. 5867-5883
Author(s):  
Naruhiko Aizawa ◽  
Tatsuo Kobayashi ◽  
Haru-Tada Sato
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
String Theory ◽  
Virasoro Algebra ◽  
Two Dimensional ◽  
Supersymmetric Extension ◽  
Conformal Field ◽  
Deformed Algebra ◽  
Deformed Virasoro Algebra

Based on the quantum superspace construction of q-deformed algebra, we discuss a supersymmetric extension of the deformed Virasoro algebra, which is a subset of the q–W∞ algebra which recently appeared in the context of two-dimensional string theory. We analyze two types of deformed super Virasoro algebra as well as their osp(1,2) subalgebras. Applying our quantum superspace structure to conformal field theory, we find the same type of deformation of affine sl(2) algebra.

INTEGRABLE SYSTEMS AND DOUBLE-LOOP ALGEBRAS IN STRING THEORY

1991 ◽  
Vol 06 (16) ◽  
pp. 1525-1531 ◽  
Author(s):  
A. MOROZOV
Keyword(s):  
String Theory ◽  
Integrable Systems ◽  
Integrable Models ◽  
Lagrangian Approach ◽  
Double Loop ◽  
Loop Algebras ◽  
Quantum Deformations ◽  
Conformal Models

Entire string theory in the formalism of first quantization cannot be exhausted by the theory of conformal models (CFTs). It is hardly enough to add only 2-dimensional integrable systems. However, examination of these systems may be of use for future guesses and generalizations. The first purpose is to give a unified treatment of all conformal and integrable models. Some steps in this direction are described in the context of Lagrangian approach. The main implication is the need to study 2-loop algebras (like those of fields on [Formula: see text] surfaces) and their quantum deformations.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

2018 ◽  
Vol 13 (3) ◽  
pp. 59-63 ◽  
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Gas Dynamics ◽  
Hydrodynamic Type ◽  
System Of Equations ◽  
Two Dimensional ◽  
Equations Of Gas Dynamics ◽  
Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

scholarly journals Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

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 Folding of Hitchin Systems and Crepant Resolutions

2021 ◽  
Author(s):  
Florian Beck ◽  
Ron Donagi ◽  
Katrin Wendland
Keyword(s):  
Fixed Point ◽  
Lie Algebras ◽  
Integrable Systems ◽  
Trace Back ◽  
Dynkin Diagrams ◽  
Or Groups ◽  
Hitchin Systems ◽  
Singular Fibers ◽  
Crepant Resolutions ◽  
Intermediate Jacobian

Abstract Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of $\textrm{ABCDEFG}$-types. This folding procedure allows to trace back the properties of the corresponding simple Lie algebras or groups to those of $\textrm{ADE}$-type. In this article, we implement the techniques of folding by graph automorphisms for Hitchin integrable systems. We show that the fixed point loci of these automorphisms are isomorphic as algebraic integrable systems to the Hitchin systems of the folded groups away from singular fibers. The latter Hitchin systems are isomorphic to the intermediate Jacobian fibrations of Calabi–Yau orbifold stacks constructed by the 1st author. We construct simultaneous crepant resolutions of the associated singular quasi-projective Calabi–Yau three-folds and compare the resulting intermediate Jacobian fibrations to the corresponding Hitchin systems.

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