Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics C

FUNDAMENTAL PROBLEMS OF SU(2)_ι WZW MODELS

Ang P

Published Jan 1, 1990• 0 citations
OpenAlex

Abstract

In this paper, we give a solution to fundamental problems of Wess-Zumino-Witten model for the case j_(?) = l and the method of solving the fundamental problems for the general case. We find also the explicit connection between the crossing matrix of SU(2)_r WZW model and the braid matrix of SL(2, q) quantum group, the latter is just the quantum Racah coefficient.

Related papers

General solutions to fundamental problems of SU(2)kWZW models

Bo-Yu Hou, Kang Li, Pei Wang

The authors give solutions to fundamental problems of the Wess-Zumino-Witten model for general cases. They also find the explicit connection between the crossing matrices of the SU(2) k WZW model and the crossing matrices of the SL(2,q) quantum group; the latter are the quantum Racah coefficients.

Journal of Physics A Mathematical and General•Aug 7, 1990•0 citations

Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions

Adam Nahum

We suggest the possibility that the two-dimensional $\mathrm{SU}{(2)}_{k}$ Wess-Zumino-Witten (WZW) theory, which has global $\mathrm{SO}(4)$ symmetry, can be continued to $2+\ensuremath{\epsilon}$ dimensions by enlarging the symmetry to $\mathrm{SO}(4+\ensuremath{\epsilon})$. This is motivated by the three-dimensional sigma model with $\mathrm{SO}(5)$ symmetry and a WZW term, which is relevant to deconfined criticality. If such a continuation exists, the structure of the renormalization group flows at small $\ensuremath{\epsilon}$ may be fixed by assuming analyticity in $\ensuremath{\epsilon}$. This leads to the conjecture that the WZW fixed point annihilates with a new, unstable fixed point at a critical dimensionality ${d}_{c}>2$. We suggest that ${d}_{c}<3$ for all $k$, and we compute ${d}_{c}$ in the limit of large $k$. The flows support the conjecture that the deconfined phase transition in $\mathrm{SU}(2)$ magnets is a ``pseudocritical'' point with approximate $\mathrm{SO}(5)$, controlled by a fixed point slightly outside the physical parameter space.

arXiv:1912.13468•Physical review. B./Physical review. B•Nov 30, 2020•80 citations

Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models

Pasquale Calabrese, Jérôme Dubail, Sara Murciano

A bstract We consider the problem of the decomposition of the Rényi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models. We first consider SU(2) k as a case study and then generalise to an arbitrary non-abelian Lie group. We find that at leading order in the subsystem size L the entanglement is equally distributed among the different sectors labelled by the irreducible representation of the associated algebra. We also identify the leading term that breaks this equipartition: it does not depend on L but only on the dimension of the representation. Moreover, a log log L contribution to the Rényi entropies exhibits a universal prefactor equal to half the dimension of the Lie group.

arXiv:2106.15946•Journal of High Energy Physics•Oct 7, 2021•82 citations

From SU ( 2 ) 5 to SU ( 2 ) 3 Wess-Zumino-Witten transitions in a frustrated spin- 5 2 chain

Natalia Chepiga, Ian K. Affleck, Frédéric Mila

The authors have identified critical points in the Wess-Zumino-Witten (WZW) SU(2)${}_{5}$ universality class in the phase diagram of a spin-5/2 chain with frustrated next-nearest-neighbor and 3-site interactions, providing a concrete example of this universality class in a realistic, nonintegrable model. These points lie on a transition line to a dimerized phase and occur when the transition turns from first order into WZW SU(2)${}_{3}$ in agreement with the generic possibilities allowed by field theory arguments.

arXiv:2202.05087•Physical review. B./Physical review. B•May 5, 2022•13 citations

Two-point spin-1/2-spin-1/2s s^l(2,ℂ) conformal Kac-Moody blocks on the torus and their monodromies

John Manolis Smyrmilds

Two issues of the SU(2) Wess-Zumino-Witten model are examined here, namely the computation of the untwisted conformal Kac-Moody blocks on the torus and their monodromy representations. Using the free field representation developed by Bernard and Felder, an integral representation of the twisted two point spin-1/2-spin-1/2 conformal Kac-Moody blocks on the torus is computed. From this, an integral representation of the untwisted blocks is computed after careful removal of infinities. Finally, the untwisted blocks are used to get a representation of the Braid Group on the torus on two strings, in terms of quantum group q-numbers.

Nuclear Physics B•Oct 1, 1995•2 citations

Quantum spin models for the SU ( n ) 1 Wess–Zumino–Witten model

Hong-Hao Tu, Anne E. B. Nielsen, Germán Sierra

We propose 1D and 2D lattice wave functions constructed from the SU(n)1 Wess–Zumino–Witten (WZW) model and derive their parent Hamiltonians. When all spins in the lattice transform under SU(n) fundamental representations, we obtain a two-body Hamiltonian in 1D, including the SU(n) Haldane–Shastry model as a special case. In 2D, we show that the wave function converges to a class of Halperin's multilayer fractional quantum Hall states and belongs to chiral spin liquids. Our result reveals a hidden SU(n) symmetry for this class of Halperin states. When the spins sit on bipartite lattices with alternating fundamental and conjugate representations, we provide numerical evidence that the state in 1D exhibits quantum criticality deviating from the expected behaviors of the SU(n)1 WZW model, while in 2D they are chiral spin liquids being consistent with the prediction of the SU(n)1 WZW model.

arXiv:1405.2950•Nuclear Physics B•Jul 5, 2014•46 citations
In this paper, we give a solution to fundamental problems of Wess-Zumino-Witten model for the case j_(?) = l and the method of solving the fundamental problems for the general case. We find also the explicit connection between the crossing matrix of SU(2)_r WZW model and the braid matrix of SL(2, q) quantum group, the latter is just the quantum Racah coefficient.
We suggest the possibility that the two-dimensional SU(2)k\mathrm{SU}{(2)}_{k}SU(2)k​ Wess-Zumino-Witten (WZW) theory, which has global SO(4)\mathrm{SO}(4)SO(4) symmetry, can be continued to $2+\ensuremath{\epsilon}$ dimensions by enlarging the symmetry to $\mathrm{SO}(4+\ensuremath{\epsilon})$. This is motivated by the three-dimensional sigma model with SO(5)\mathrm{SO}(5)SO(5) symmetry and a WZW term, which is relevant to deconfined criticality. If such a continuation exists, the structure of the renormalization group flows at small $\ensuremath{\epsilon}$ may be fixed by assuming analyticity in $\ensuremath{\epsilon}$. This leads to the conjecture that the WZW fixed point annihilates with a new, unstable fixed point at a critical dimensionality dc>2{d}_{c}>2dc​>2. We suggest that dc<3{d}_{c}<3dc​<3 for all kkk, and we compute dc{d}_{c}dc​ in the limit of large kkk. The flows support the conjecture that the deconfined phase transition in SU(2)\mathrm{SU}(2)SU(2) magnets is a ``pseudocritical'' point with approximate SO(5)\mathrm{SO}(5)SO(5), controlled by a fixed point slightly outside the physical parameter space.
A bstract We consider the problem of the decomposition of the Rényi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models. We first consider SU(2) k as a case study and then generalise to an arbitrary non-abelian Lie group. We find that at leading order in the subsystem size L the entanglement is equally distributed among the different sectors labelled by the irreducible representation of the associated algebra. We also identify the leading term that breaks this equipartition: it does not depend on L but only on the dimension of the representation. Moreover, a log log L contribution to the Rényi entropies exhibits a universal prefactor equal to half the dimension of the Lie group.
The authors have identified critical points in the Wess-Zumino-Witten (WZW) SU(2)5{}_{5}5​ universality class in the phase diagram of a spin-5/2 chain with frustrated next-nearest-neighbor and 3-site interactions, providing a concrete example of this universality class in a realistic, nonintegrable model. These points lie on a transition line to a dimerized phase and occur when the transition turns from first order into WZW SU(2)3{}_{3}3​ in agreement with the generic possibilities allowed by field theory arguments.
Two issues of the SU(2) Wess-Zumino-Witten model are examined here, namely the computation of the untwisted conformal Kac-Moody blocks on the torus and their monodromy representations. Using the free field representation developed by Bernard and Felder, an integral representation of the twisted two point spin-1/2-spin-1/2 conformal Kac-Moody blocks on the torus is computed. From this, an integral representation of the untwisted blocks is computed after careful removal of infinities. Finally, the untwisted blocks are used to get a representation of the Braid Group on the torus on two strings, in terms of quantum group q-numbers.
We propose 1D and 2D lattice wave functions constructed from the SU(n)1 Wess–Zumino–Witten (WZW) model and derive their parent Hamiltonians. When all spins in the lattice transform under SU(n) fundamental representations, we obtain a two-body Hamiltonian in 1D, including the SU(n) Haldane–Shastry model as a special case. In 2D, we show that the wave function converges to a class of Halperin's multilayer fractional quantum Hall states and belongs to chiral spin liquids. Our result reveals a hidden SU(n) symmetry for this class of Halperin states. When the spins sit on bipartite lattices with alternating fundamental and conjugate representations, we provide numerical evidence that the state in 1D exhibits quantum criticality deviating from the expected behaviors of the SU(n)1 WZW model, while in 2D they are chiral spin liquids being consistent with the prediction of the SU(n)1 WZW model.