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We build the Z$_{3}$ invariants fusion rules associated to the (D$_{4}$,A$_{6}$) conformal algebra. This algebra is known to describe the tri-critical Potts model. The 4-pt correlation functions of critical fields are developed in the bootstrap approach, and in the other hand, they are written in term of integral representation of the conformal blocks. By comparing both the expressions, one can determine the structure constantes of the operator algebra.
The bootstrap determination of the geometrical correlation functions in the two-dimensional Potts model proposed in a paper [arXiv:1607.07224] was later shown in [arXiv:1809.02191] to be incorrect, the actual spectrum of the model being considerably
We consider a multi-scalar field theory with either short-range or long-range free action and with quartic interactions that are invariant under $O(N_1)times O(N_2) times O(N_3)$ transformations, of which the scalar fields form a tri-fundamental repr
In this work, we exploit the operator content of the $(D_{4}, A_{6})$ conformal algebra. By constructing a $Z_{2}$-invariants fusion rules of a chosen subalgebra and by resolving the bootstrap equations consistent with these rules, we determine the structure constants of the subalgebra.
Low frequency perturbations at the boundary of critical quantum chains can be understood in terms of the sequence of boundary conditions imposed by them, as has been previously demonstrated in the Ising and related fermion models. Using extensive num
Any two-dimensional infinite regular lattice G can be produced by tiling the plane with a finite subgraph B of G; we call B a basis of G. We introduce a two-parameter graph polynomial P_B(q,v) that depends on B and its embedding in G. The algebraic c