arXiv subjects
Publications and source records attributed to Vladimir S. Dotsenko.
Correlation function is defined and calculated for the punctual states of the fermion supersymmetric string (N=1), in its critical dimension D=10.
Under the assumption that the product of two spin operators decomposes uniquely into the degenerate conformal fields $\{Φ_{n',n}\}$, the general expression for the correlation function of four spins is defined for the $q$ states Potts model with $q$ taking general values in the interval $1 \leq q \leq 4$. The limit of $q \rightarrow 1$ is considered in detail and the four spins function is obtained for the percolation model.
By using the Coulomb gas technics we calculate the four-spin correlation function in the percolation $q\rightarrow 1$ limit of the Potts model. It is known that the four-point functions define the actual fusion rules of a particular model. In this respect, we find that fusion of two spins, of dimension $Δ_σ=\frac{5}{96}$, produce a new channel, in the 4-point function, which is due to the operator with dimension $Δ=5/8$.
It is shown that the general 3-point function $<Φ_{a} Φ_{b} Φ_{c}>$, with continuous values of charges $a, b, c$ of a statistical model operators, and the 3-point function of the Liouville model, could all be obtained by successive analytical continuations starting from the 3-point function of the minimal model.
We analyze, and prove, the associativity of the new Z_{3} parafermionic chiral algebra which has been announced some time ago, with principal parafermionic fields having the conformal dimension Δ_ψ=8/3. In doing so we have developed a new method for analyzing the associativity of a given chiral algebra of parafermionic type, the method which might be of a more general significance than a particular conformal field theory studied in detail in this paper. Still, even in the context of our particular chiral algebra, of Z_{3} parafermions with Δ_ψ=8/3, the new method allowed us to give a proof of associativity which we consider to be complete.
In this paper, which is the second one in a series of two papers, we shall present two more solutions, non-minimal ones, for the Z_{3} parafermionic chiral algebra with Delta_{psi}=Delta_{psi^{+}}=8/3, psi(z), psi^{+}(z) being the principal parafermionic fields.
Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry $Z_{N}$, for N odd. New fixed points are found and classified.
Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry $Z\_{5}$. New fixed points are found and classified.
We have constructed the parafermionic chiral algebra with the principal parafermionic fields Ψ,Ψ^{+} having the conformal dimension Δ_Ψ=8/3 and realizing the symmetry Z_{3}.
$N$ conformal theory models $WD^{(p)}_{3}$ coupled locally by their energy operators are analyzed by means of a perturbative renormalization group. New non-trivial fixed points are found.
We have studied the conformal models WD_{n}^{(p)}, n=3,4,5,..., in the presence of disorder which couples to the energy operator of the model. In the limit of p<<1 where p is the corresponding minimal model index, the problem could be analyzed by means of the perturbative renormalization group, with $epsilon$-expansion in $ε$=1/p. We have found that the disorder makes to flow the model WD_{n}^{(p)} to the model WD_{n}^{(p-1)} without disorder. In the related problem of N coupled regular WD_{n}^{(p)} models (no disorder), coupled by their energy operators, we find a flow to the fixed point of N decoupled WD_{n}^{(p-1)}. But in addition we find in this case two new fixed points which could be reached by a fine tuning of the initial values of the couplings. The corresponding critical theories realize the permutational symmetry in a non-trivial way, like this is known to be the case for coupled Potts models, and they could not be identified with the presently known conformal models.
We present a method for classifying conformal field theories based on Coulomb gases (bosonic free-field construction). Given a particular geometric configuration of the screening charges, we give necessary conditions for the existence of degenerate representations and for the closure of the vertex-operator algebra. The resulting classification contains, but is more general than, the standard one based on classical Lie algebras. We then apply the method to the Coulomb gas theory for the two-flavoured loop model of Jacobsen and Kondev. The purpose of the study is to clarify the relation between Coulomb gas models and conformal field theories with extended symmetries.