scholarly journals QUANTUM AFFINE SYMMETRY IN VERTEX MODELS

1993 ◽  
Vol 08 (08) ◽  
pp. 1479-1511 ◽  
Author(s):  
MAKOTO IDZUMI ◽  
TETSUJI TOKIHIRO ◽  
KENJI IOHARA ◽  
MICHIO JIMBO ◽  
TETSUJI MIWA ◽  
...  
Keyword(s):  
Representation Theory ◽  
Tensor Product ◽  
Spin Chain ◽  
Vertex Model ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Affine Symmetry ◽  
Higher Spin ◽  
Local Operators ◽  
The One

We study the higher spin analogs of the six-vertex model on the basis of its symmetry under the quantum affine algebra [Formula: see text]. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer matrix, vacuum, creation/ annihilation operators of particles, and local operators, purely in the language of representation theory. We find that, regardless of the level of the representation involved, the particles have spin 1/2, and that the n-particle space has an RSOS type structure rather than a simple tensor product of the one-particle space. This agrees with the picture proposed earlier by Reshetikhin.

Six-Vertex Model

2019 ◽  
pp. 454-473
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Spin Chain ◽  
Quantum Spin ◽  
Square Lattice ◽  
Vertex Model ◽  
Quantum Spin Chain ◽  
Special Value ◽  
Quantum Operators ◽  
The One

This chapter considers the special case of the six-vertex model on a square lattice using a trigonometric parameterization of the vertex weights. It demonstrates how, by exploiting the Yang-Baxter relations, the six-vertex model is diagonalized and the Bethe ansatz equations are derived. The Hamiltonian of the Heisenberg quantum spin chain is obtained from the transfer matrix for a special value of the spectral parameter together with an infinite set of further conserved quantum operators. By the diagonalization of the transfer matrix the exact solution of the one-dimensional quantum spin chain Hamiltonian has automatically also been obtained, which is given by the same Bethe ansatz equations.

scholarly journals A functional model for the tensor product of level 1 highest and level −1 lowest modules for the quantum affine algebra Uq(sl2)

2004 ◽  
Vol 25 (8) ◽  
pp. 1197-1229 ◽  
Author(s):  
B. Feigin ◽  
M. Jimbo ◽  
M. Kashiwara ◽  
T. Miwa ◽  
E. Mukhin ◽  
...  
Keyword(s):  
Tensor Product ◽  
Functional Model ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Level 1

scholarly journals Integrable boundary states in D3-D5 dCFT: beyond scalars

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Charlotte Kristjansen ◽  
Dennis Müller ◽  
Konstantin Zarembo
Keyword(s):  
Perturbation Theory ◽  
Domain Wall ◽  
Gauge Group ◽  
Spin Chain ◽  
Boundary State ◽  
Boundary States ◽  
Local Operators ◽  
Set Up ◽  
The One

Abstract A D3-D5 intersection gives rise to a defect CFT, wherein the rank of the gauge group jumps by k units across a domain wall. The one-point functions of local operators in this set-up map to overlaps between on-shell Bethe states in the underlying spin chain and a boundary state representing the D5 brane. Focussing on the k = 1 case, we extend the construction to gluonic and fermionic sectors, which was prohibitively difficult for k > 1. As a byproduct, we test an all-loop proposal for the one-point functions in the su(2) sector at the half-wrapping order of perturbation theory.

Two-parameter Quantum Affine Algebra $U_{r,s}(\widehat{\frak{sl}}_2)$

2013 ◽  
Vol 20 (03) ◽  
pp. 507-514 ◽  
Author(s):  
Honglian Zhang ◽  
Ruzhi Pang
Keyword(s):  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Evaluation Representation ◽  
The One ◽  
Parameter Case ◽  
Two Parameter

We give two realizations of the two-parameter quantum affine algebra [Formula: see text] and prove that its structure is isomorphic to the one-parameter case. In particular, the evaluation representation of [Formula: see text] is obtained.

scholarly journals Simplicity of heads and socles of tensor products

2014 ◽  
Vol 151 (2) ◽  
pp. 377-396 ◽  
Author(s):  
Seok-Jin Kang ◽  
Masaki Kashiwara ◽  
Myungho Kim ◽  
Se-jin Oh
Keyword(s):  
Tensor Product ◽  
Hecke Algebras ◽  
Tensor Products ◽  
Convolution Product ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Simple Modules

AbstractWe prove that, for simple modules $M$ and $N$ over a quantum affine algebra, their tensor product $M\otimes N$ has a simple head and a simple socle if $M\otimes M$ is simple. A similar result is proved for the convolution product of simple modules over quiver Hecke algebras.

scholarly journals The integrable (hyper)eclectic spin chain

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Changrim Ahn ◽  
Matthias Staudacher
Keyword(s):  
Spin Chain ◽  
Nearest Neighbor ◽  
Inverse Scattering Method ◽  
Spin Chains ◽  
Scattering Method ◽  
Yang Mills ◽  
Deformation Parameters ◽  
Dilatation Operator ◽  
The One ◽  
State Spin

Abstract We refine the notion of eclectic spin chains introduced in [1] by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians. They turn out to be non-diagonalizable in the multiparticle sector (n > 2), where their “spectrum” consists of an intricate collection of Jordan blocks of arbitrary size and multiplicity. We show how and why the quantum inverse scattering method, sought to be universally applicable to integrable nearest-neighbor spin chains, essentially fails to reproduce the details of this spectrum. We then provide, for n=3, detailed evidence by a variety of analytical and numerical techniques that the spectrum is not “random”, but instead shows surprisingly subtle and regular patterns that moreover exhibit universality for generic deformation parameters. We also introduce a new model, the hypereclectic spin chain, where all parameters are zero except for one. Despite the extreme simplicity of its Hamiltonian, it still seems to reproduce the above “generic” spectra as a subset of an even more intricate overall spectrum. Our models are inspired by parts of the one-loop dilatation operator of a strongly twisted, double-scaled deformation of $$ \mathcal{N} $$ N = 4 Super Yang-Mills Theory.

THE AFFINE N = 4 YANG–MILLS THEORY

1992 ◽  
Vol 07 (11) ◽  
pp. 2469-2485
Author(s):  
A. C. CADAVID ◽  
R. J. FINKELSTEIN
Keyword(s):  
Mass Spectrum ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Effective Theory ◽  
Affine Algebra ◽  
Linear Mass ◽  
Expectation Value ◽  
Yang Mills ◽  
Exotic States ◽  
Affine Symmetry

An affine field theory may be constructed by gauging an affine algebra. The momentum integrals of the affine N = 4 Yang–Mills theory are ultraviolet finite but diverge because the sum over states is infinite. If the affine symmetry is broken by postulating a nonvanishing vacuum expectation value for that component of the scalar field lying in the L0 direction, then the theory acquires a linear mass spectrum. This broken theory is ultraviolet finite too, but the mass spectrum is unbounded. If it is also postulated that the mass spectrum has an upper bound (say, the Planck mass), then the resulting theory appears to be altogether finite. The influence of the exotic states has been estimated and, according to the proposed scenario, is negligible below energies at which gravitational interactions become important. The final effective theory has the symmetry of a compact Lie algebra augmented by the operator L0.

scholarly journals Kerr-Newman stress-tensor from minimal coupling

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Ming-Zhi Chung ◽  
Yu-tin Huang ◽  
Jung-Wook Kim
Keyword(s):  
Form Factor ◽  
Stress Tensor ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Minimal Coupling ◽  
Massive Spin ◽  
Stress Energy ◽  
Newman Black Hole ◽  
Higher Spin ◽  
The One

Abstract In this paper, we demonstrate that at leading order in post Minkowskian (PM) expansion, the stress-energy tensor of Kerr-Newman black hole can be recovered to all orders in spin from three sets of minimal coupling: the electric and gravitational minimal coupling for higher-spin particles, and the “minimal coupling” for massive spin-2 decay. These couplings are uniquely defined from kinematic consideration alone. This is shown by extracting the classical piece of the one-loop stress-energy tensor form factor, which we provide a basis that is valid to all orders in spin. The 1 PM stress tensor, and the metric in the harmonic gauge, is then recovered from the classical spin limit of the form factor.

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