Conformal Field Theory and Hyperbolic Geometry
Copyright policy )Conformal Field Theory and Hyperbolic Geometry
We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic length, we motivate a reformulation of the basic equation of conformal covariance. The scale factors gain a new, physical interpretation. We exhibit a fully factored form for the three-point function. A doubly-infinite discrete series of central charges with limit c=-2 is discovered. A correspondence between the anomalous dimension and the angle of certain hyperbolic figures emerges. Note: email after 12/19: kleban@maine.maine.edu
7 pages (PlainTeX)
- University of Maine United States
- University of Massachusetts System United States
- Institute for Advanced Study United States
High Energy Physics - Theory, High Energy Physics - Theory (hep-th), Condensed Matter (cond-mat), FOS: Physical sciences, Classical or axiomatic geometry and physics, Condensed Matter, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Continuum limits in quantum field theory
High Energy Physics - Theory, High Energy Physics - Theory (hep-th), Condensed Matter (cond-mat), FOS: Physical sciences, Classical or axiomatic geometry and physics, Condensed Matter, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Continuum limits in quantum field theory
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