• Corpus ID: 118908819

Conformal Field Theory, Vertex Operator Algebra and Stochastic Loewner Evolution in Ising Model

@article{Zahabi2015ConformalFT,
  title={Conformal Field Theory, Vertex Operator Algebra and Stochastic Loewner Evolution in Ising Model},
  author={Ali Zahabi},
  journal={arXiv: Mathematical Physics},
  year={2015}
}
  • A. Zahabi
  • Published 6 May 2015
  • Mathematics
  • arXiv: Mathematical Physics
We review the algebraic and analytic aspects of the conformal field theory (CFT) and its relation to the stochastic Loewner evolution (SLE) in an example of the Ising model. We obtain the scaling limit of the correlation functions of Ising free fermions on an arbitrary simply connected two-dimensional domain $D$. Then, we study the analytic and algebraic aspects of the fermionic CFT on $D$, using the Fock space formalism of fields, and the Clifford vertex operator algebra (VOA). These… 
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References

SHOWING 1-10 OF 29 REFERENCES

Conformal Transformations and the SLE Partition Function Martingale

Abstract. We present an implementation in conformal field theory (CFT) of local finite conformal transformations fixing a point. We give explicit constructions when the fixed point is either the

Discrete holomorphicity and Ising model operator formalism

We explore the connection between the transfer matrix formalism and discrete complex analysis approach to the two dimensional Ising model. We construct a discrete analytic continuation matrix,

Stochastic geometry of critical curves, Schramm–Loewner evolutions and conformal field theory

Conformally invariant curves that appear at critical points in two-dimensional statistical mechanics systems and their fractal geometry have received a lot of attention in recent years. On the one

Universality in the 2D Ising model and conformal invariance of fermionic observables

It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no

Discrete Holomorphicity at Two-Dimensional Critical Points

After a brief review of the historical role of analyticity in the study of critical phenomena, an account is given of recent discoveries of discretely holomorphic observables in critical

Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model

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

Conformally Invariant Processes in the Plane

Theoretical physicists have predicted that the scaling limits of many two-dimensional lattice models in statistical physics are in some sense conformally invariant. This belief has allowed physicists

The energy density in the planar Ising model

We study the critical Ising model on the square lattice in bounded simply connected domains with + and free boundary conditions. We relate the energy density of the model to a discrete fermionic

Conformal Invariance of Ising Model Correlations

We review recent results with D. Chelkak and K. Izyurov, where we rigorously prove existence and conformal invariance of scaling limits of magnetization and multi-point spin correlations in the

Vertex algebras, Kac-Moody algebras, and the Monster.

  • R. Borcherds
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1986
An integral form is constructed for the universal enveloping algebra of any Kac-Moody algebras that can be used to define Kac's groups over finite fields, some new irreducible integrable representations, and a sort of affinization of anyKac-moody algebra.