We develop a general method of solving non-trivial conformal field theories by coset imbeddings into free boson models. In particular, we consider ZN parafermion models represented by the coset model constructions su(N1)⊕su(N)1/su(N)2, and bosonize the su(N)1 models. The calculation of correlation functions of these parafermion theories is formulated so that detailed information from the diagonal su(N)2 theory is not required. A differential equation for the four-point functionof order operators σ1 is derived as an example. We also derive differential equations with respect to the modular parameter τ for the parafermion characters in terms of the su(N)1 characters only. In particular, the equations for the Z2 and Z3 characters are first and second order respectively.We develop a general method of solving non-trivial conformal field theories by coset imbeddings into free boson models. In particular, we consider ZN parafermion models represented by the coset model constructions su(N1)⊕su(N)1/su(N)2, and bosonize the su(N)1 models. The calculation of correlation functions of these parafermion theories is formulated so that detailed information from the diagonal su(N)2 theory is not required. A differential equation for the four-point functionof order operators σ1 is derived as an example. We also derive differential equations with respect to the modular parameter τ for the parafermion characters in terms of the su(N)1 characters only. In particular, the equations for the Z2 and Z3 characters are first and second order respectively.

Nuclear Physics BSep 1, 198924 citations

A lattice model for the second $\mathbb{Z}_{3}$ parafermionic field theoryA lattice model for the second $\mathbb{Z}_{3}$ parafermionic field theory

Benoit Estienne

The second $\mathbb{Z}_{3}$ parafermionic conformal theories are associated with the coset construction $\frac{SU(2)_{k}\times SU(2)_{4}}{SU(2)_{k+4}} $. Solid-on-solid integrable lattice models obtained by fusion of the model based on level-1 representation of the affine algebra $B_1^{(1)}$ have a critical point described by these conformal theories. Explicit values for the Boltzmann weights are derived for these models, and it is shown that the Boltzmann weights can be made positive for a particular value of the spectral parameter, opening a way to eventual numerical simulations of these conformal field theories. Away from criticality, these lattice models describe an integrable, massive perturbation of the parafermionic conformal theory by the relevant field $Ψ_{-2/3}^{\dagger}D_{1,3} $.The second $\mathbb{Z}_{3}$ parafermionic conformal theories are associated with the coset construction $\frac{SU(2)_{k}\times SU(2)_{4}}{SU(2)_{k+4}} $. Solid-on-solid integrable lattice models obtained by fusion of the model based on level-1 representation of the affine algebra $B_1^{(1)}$ have a critical point described by these conformal theories. Explicit values for the Boltzmann weights are derived for these models, and it is shown that the Boltzmann weights can be made positive for a particular value of the spectral parameter, opening a way to eventual numerical simulations of these conformal field theories. Away from criticality, these lattice models describe an integrable, massive perturbation of the parafermionic conformal theory by the relevant field $Ψ_{-2/3}^{\dagger}D_{1,3} $.

arXiv:0812.3473Dec 18, 20080 citations

A lattice model for the second

\mathbb{Z}_{3}

parafermionic field theory

The second

\mathbb{Z}_{3}

parafermionic conformal theories are associated with the coset construction $\frac{SU(2)_{k}\times SU(2)_{4}}{SU(2)_{k+4}} $. Solid-on-solid integrable lattice models obtained by fusion of the model based on level-1 representation of the affine algebra

B_1^{(1)}

have a critical point described by these conformal theories. Explicit values for the Boltzmann weights are derived for these models, and it is shown that the Boltzmann weights can be made positive for a particular value of the spectral parameter, opening a way to eventual numerical simulations of these conformal field theories. Away from criticality, these lattice models describe an integrable, massive perturbation of the parafermionic conformal theory by the relevant field $Ψ_{-2/3}^{\dagger}D_{1,3} $.