Holographic duality, supersymmetry, and Painleve equation
Abstract
Description
An example of the holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity theories is found. The constraints on the target space geometry of the 4d, N=2 non-linear sigma-models in N=2 supergravity background are interpreted as the renormalization flow equations in two dimensions. Our geometrical description of the renormalization flow is manifestly covariant under reparametrization of the 2d coupling constants. The proposed holography is described in terms of the (Weyl) anti-self-dual Einstein metrics, whose exact regular (Tod-Hitchin) solutions are governed by the Painleve VI equation.
LaTeX; reduced to 6 pages; invited talk given at the Fradkin Memorial Conference, Moscow, June 2000
LaTeX; reduced to 6 pages; invited talk given at the Fradkin Memorial Conference, Moscow, June 2000