scholarly journals Quantum Integrable Model of an Arrangement of Hyperplanes

2011 ◽  
Author(s):  
Alexander Varchenko
Keyword(s):  
Integrable Model ◽  
Arrangement Of Hyperplanes

scholarly journals RG flows of integrable σ-models and the twist function

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
François Delduc ◽  
Sylvain Lacroix ◽  
Konstantinos Sfetsos ◽  
Konstantinos Siampos
Keyword(s):  
Renormalization Group ◽  
Large Class ◽  
Rational Function ◽  
Integrable Model ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Non Linear ◽  
Group Flow

Abstract In the study of integrable non-linear σ-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central rôle. For a large class of such models, we show that they are one-loop renormalizable, and that the renormalization group flow equations can be written directly in terms of the twist function in a remarkably simple way. The resulting equation appears to have a universal character when the integrable model is characterized by a twist function.

scholarly journals Integrable model of a p -wave bosonic superfluid

2019 ◽  
Vol 1 (3) ◽  
Author(s):  
Sergio Lerma-Hernández ◽  
Jorge Dukelsky ◽  
Gerardo Ortiz
Keyword(s):  
Integrable Model ◽  
P Wave

scholarly journals On (2+1)-dimensional expanding integrable model of the Davey-Stewartson hierarchy

2021 ◽  
Vol 25 (6 Part B) ◽  
pp. 4431-4439
Author(s):  
Xiu-Rong Guo ◽  
Fang-Fang Ma ◽  
Juan Wang
Keyword(s):  
Lie Algebras ◽  
Hamiltonian Structure ◽  
Integrable Model ◽  
Coupling System ◽  
Integrable Coupling ◽  
Type Abstraction Hierarchy

This paper mainly investigates the reductions of an integrable coupling of the Levi hierarchy and an expanding model of the (2+1)-dimensional Davey-Stewartson hierarchy. It is shown that the integrable coupling system of the Levi hierarchy possesses a quasi-Hamiltonian structure under certain constraints. Based on the Lie algebras construct, The type abstraction hierarchy scheme is used to gener?ate the (2+1)-dimensional expanding integrable model of the Davey-Stewartson hierarchy.

scholarly journals INTEGRABILITY IN QCD AND BEYOND

2004 ◽  
Vol 19 (28) ◽  
pp. 4715-4788 ◽  
Author(s):  
A. V. BELITSKY ◽  
V. M. BRAUN ◽  
A. S. GORSKY ◽  
G. P. KORCHEMSKY
Keyword(s):  
Integrable Model ◽  
High Energy ◽  
Completely Integrable Systems ◽  
General Phenomenon ◽  
Heisenberg Spin ◽  
Yang Mills ◽  
Heisenberg Spin Chain ◽  
Regge Behavior ◽  
Hidden Symmetry ◽  
Classical Integrable

Yang–Mills theories in four space–time dimensions possess a hidden symmetry which does not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum level. It turns out that the effective Yang–Mills dynamics in several important limits is described by completely integrable systems that prove to be related to the celebrated Heisenberg spin chain and its generalizations. In this review we explain the general phenomenon of complete integrability and its realization in several different situations. As a prime example, we consider in some detail the scale dependence of composite (Wilson) operators in QCD and super-Yang–Mills (SYM) theories. High-energy (Regge) behavior of scattering amplitudes in QCD is also discussed and provides one with another realization of the same phenomenon that differs, however, from the first example in essential details. As the third example, we address the low-energy effective action in a [Formula: see text] SYM theory which, contrary to the previous two cases, corresponds to a classical integrable model. Finally, we include a short overview of recent attempts to use gauge/string duality in order to relate integrability of Yang–Mills dynamics with the hidden symmetry of a string theory on a curved background.

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