相关论文: Chiral correlators of the Ising conformal field th…
We obtain an explicit realization of all the primary fields of the Ising model in terms of a conformal field theory of constrained fermions. The four-point correlators of the energy, order and disorder operators are explicitly calculated.
A powerful approach to the celebrated Wess-Zumino-Witten (WZW) model is provided by its free-field realization. However, explicit calculations of conformal blocks are not described in the literature in full detail. We begin this study with…
We give explicit field theoretical representations for the observables of 2+1 dimensional Chern-Simons theory in terms of gauge invariant composites of 2D WZW fields. To test our identification we compute some basic Wilson loop correlators…
We construct discrete holomorphic observables in the Ising model at criticality and show that they have conformally covariant scaling limits (as mesh of the lattice tends to zero). In the sequel those observables are used to construct…
We consider the free field approach or bosonization technique for the Wess-Zumino-Novikov-Witten model with arbitrary Kac-Moody algebra on Riemann surface of genus zero. This subject was much studied previously, and the paper can be…
We present exact combinatorial versions of bosonization identities, which equate the product of two Ising correlators with a free field (bosonic) correlator. The role of the discrete free field is played by the height function of an…
We use the conformal Ward identities to study the structure of correlation functions in coset conformal field theories. For a large class of primary fields of arbitrary g/h theory a factorization anzatz is found.Corresponding correlation…
A general procedure is presented to determine, given any suitable representation of the modular group, the characters of all possible Rational Conformal Field Theories whose associated modular representation is the given one. The relevant…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
Working in the axiomatic framework recently proposed by Gaberdiel and Goddard, we prove a generalized version of Zhu's Theorem; for any chiral bosonic conformal field theory on the sphere, our result characterizes the chiral blocks in terms…
Work of Buczynska, Wisniewski, Sturmfels and Xu, and the second author has linked the group-based phylogenetic statistical model associated with the group Z/2Z with the Wess-Zumino-Witten (WZW) model of conformal field theory associated to…
In this note we overview recent convergence results for correlations in the critical planar nearest-neighbor Ising model. We start with a short discussion of the combinatorics of the model and a definition of fermionic and spinor…
The generalized Knizhnik-Zamolodchikov equations of irrational conformal field theory provide a uniform description of rational and irrational conformal field theory. Starting from the known high-level solution of these equations, we first…
We give an explicit description of "bundles of conformal blocks" in Wess-Zumino-Witten models of Conformal field theory and prove that integral representations of Knizhnik-Zamolodchikov equations constructed earlier by the second and third…
We prove bosonization identities for the scaling limits of the critical Ising correlations in finitely-connected planar domains, expressing those in terms of correlations of the compactified Gaussian free field. This, in particular, yields…
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding…
The fuzzy-sphere regularisation is a powerful tool to study conformal field theories (CFT) in three spacetime dimensions. In this paper, we extend its scope to CFTs with local fermionic operators. We realise the free-Majorana-fermion CFT on…
It is shown that Weyl spinors in 4D Minkowski space are composed of primary fields of half-integer conformal weights. This yields representations of fermionic 2-point functions in terms of correlators of primary fields with a factorized…
The $d=2$ critical Ising model is described by an exactly solvable Conformal Field Theory (CFT). The deformation to $d=2+\epsilon$ is a relatively simple system at strong coupling outside of even dimensions. Using novel numerical and…
Correlation functions of the two-dimensional Ising model on the periodic lattice can be expressed in terms of form factors - matrix elements of the spin operator in the basis of common eigenstates of the transfer matrix and translation…