Abstract
Lattice radial quantization is introduced as a nonperturbative method intended to numerically solve Euclidean conformal field theories that can be realized as fixed points of known Lagrangians. As an example, we employ a lattice shaped as a cylinder with a 2D Icosahedral cross-section to discretize dilatations in the 3D Ising model. Using the integer spacing of the anomalous dimensions of the first two descendants (l=1,2), we obtain an estimate for η=0.034(10). We also observed small deviations from integer spacing for the 3rd descendant, which suggests that a further improvement of our radial lattice action will be required to guarantee conformal symmetry at the Wilson–Fisher fixed point in the continuum limit.
Highlights
Conformal field theories are theoretically interesting in their own right, have applications in Condensed Matter and Statistical Physics and are relevant to Particle Physics in general
Using the 3D Ising model, we carry out a modest numerical test of lattice radial quantization of the Wilson-Fisher fixed point field theory
The method of lattice radial quantization presented in this paper holds promise as a practical nonperturbative tool for conformal field theory
Summary
Conformal field theories are theoretically interesting in their own right, have applications in Condensed Matter and Statistical Physics and are relevant to Particle Physics in general. They may play a central role in the yet unknown correct description of Particle Physics beyond the Standard Model. The critical new feature of our proposal is to introduce a uniform lattice discretization of log(r); this provides a reasonable match between numerical resources and the relevant degrees of freedom. Using the 3D Ising model, we carry out a modest numerical test of lattice radial quantization of the Wilson-Fisher fixed point field theory
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