scholarly journals Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties

2020 ◽  
Author(s):  
Gabriele Rembado ◽  
Keyword(s):  
Hamiltonian Reduction ◽  
Representation Variety ◽  
Quiver Varieties ◽  
Classical Symmetries ◽  
Quantum Hamiltonian Reduction ◽  
Quantum Hamiltonian ◽  
Howe Duality ◽  
Casimir Connection ◽  
Group Of Symmetries

We will exhibit a group of symmetries of the simply-laced quantum connections, generalising the quantum/Howe duality relating KZ and the Casimir connection. These symmetries arise as a quantisation of the classical symmetries of the simply-laced isomonodromy systems, which in turn generalise the Harnad duality. The quantisation of the classical symmetries involves constructing the quantum Hamiltonian reduction of the representation variety of any simply-laced quiver, both in filtered and in deformation quantisation.

QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

1992 ◽  
Vol 07 (20) ◽  
pp. 4885-4898 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Quantum Hamiltonian Reduction ◽  
Free Field Realization ◽  
Coset Construction ◽  
Quantum Hamiltonian

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

REMARKS ON THE BRST QUANTIZED GAUGED WZNW MODELS AND THE TODA FIELD THEORIES

1991 ◽  
Vol 06 (10) ◽  
pp. 885-891 ◽  
Author(s):  
NOBUHARU HAYASHI
Keyword(s):  
Coupling Constants ◽  
Field Theories ◽  
Hamiltonian Reduction ◽  
Quantum Hamiltonian Reduction ◽  
Quantum Hamiltonian

It is shown that the quantum Hamiltonian reduction proposed by Bershadsky and Ooguri enables us to connect the gauged WZNW models with fractional levels to the quantum Toda field theories, and the coupling constants of the Toda field theories with the fractional levels. The BRST framework is applied to the SL (n, ℝ)-WZNW models.

scholarly journals Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI

2021 ◽  
Author(s):  
Fatane Mobasheramini ◽  
◽  
Marco Bertola ◽  
Keyword(s):  
Canonical Quantization ◽  
Classical Case ◽  
Particle Systems ◽  
Integral Representations ◽  
Painlevé Equations ◽  
Hamiltonian Reduction ◽  
Painleve Equations ◽  
Special Representation ◽  
Quantum Hamiltonian Reduction ◽  
Quantum Hamiltonian

We consider the isomonodromic formulation of the Calogero-Painlevé multi-particle systems and proceed to their canonical quantization. We then proceed to the quantum Hamiltonian reduction on a special representation to radial variables, in analogy with the classical case and also with the theory of quantum Calogero equations. This quantized version is compared to the generalization of a result of Nagoya on integral representations of certain solutions of the quantum Painlevé equations. We also provide multi-particle generalizations of these integral representations.

scholarly journals DERIVATIONS OF THE TRIGONOMETRIC BCn SUTHERLAND MODEL BY QUANTUM HAMILTONIAN REDUCTION

2010 ◽  
Vol 22 (06) ◽  
pp. 699-732 ◽  
Author(s):  
L. FEHÉR ◽  
B. G. PUSZTAI
Keyword(s):  
Laplace Operator ◽  
Coupling Constants ◽  
Hamiltonian Reduction ◽  
Real Form ◽  
Quantum Hamiltonian Reduction ◽  
Quantum Hamiltonian ◽  
Sutherland Model ◽  
The Laplace Operator ◽  
Vector Valued Functions ◽  
Vector Valued

The BCn Sutherland Hamiltonian with coupling constants parametrized by three arbitrary integers is derived by reductions of the Laplace operator of the group U(N). The reductions are obtained by applying the Laplace operator on spaces of certain vector valued functions equivariant under suitable symmetric subgroups of U(N) × U(N). Three different reduction schemes are considered, the simplest one being the compact real form of the reduction of the Laplacian of GL(2n, ℂ) to the complex BCn Sutherland Hamiltonian previously studied by Oblomkov.

THE SU(2)0 WZNW MODEL

2003 ◽  
Vol 18 (25) ◽  
pp. 4685-4702
Author(s):  
ALEXANDER NICHOLS
Keyword(s):  
Correlation Functions ◽  
Free Field ◽  
Hamiltonian Reduction ◽  
Close Correspondence ◽  
Quantum Hamiltonian Reduction ◽  
Quantum Hamiltonian ◽  
Wznw Model

We analyse the correlation functions and operator content of the SU(2)0 model using both the free field description and the solutions to the Knizhnik-Zamolodchikov equations. We show that there is a very close correspondence between this model and the well studied c=-2 theory. We also demonstrate that the quantum Hamiltonian reduction of SU(2)0 leads very directly to the correlation functions of the c=-2 model.

scholarly journals SU(2)0 AND OSp(2|2)-2 WZNW MODELS: TWO CURRENT ALGEBRAS, ONE LOGARITHMIC CFT

2002 ◽  
Vol 17 (19) ◽  
pp. 2615-2643 ◽  
Author(s):  
I. I. KOGAN ◽  
A. NICHOLS
Keyword(s):  
Correlation Functions ◽  
Boundary Effects ◽  
Hamiltonian Reduction ◽  
The Novel ◽  
Quantum Hamiltonian Reduction ◽  
Quantum Hamiltonian ◽  
Wznw Model ◽  
Current Algebras

We show that the SU (2)0 Wess–Zumino–Novikov–Witten (WZNW) model has a hidden OSp (2|2)-2 symmetry. Both these theories are known to have logarithms in their correlation functions. We also show that, like OSp(2|2)-2, the logarithmic structure present in the SU (2)0 model is due to an underlying c = - 2 sector. We demonstrate that the quantum Hamiltonian reduction of SU (2)0 leads very directly to the correlation functions of the c=-2 model. We also discuss some of the novel boundary effects which can take place in this model.

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