Exact C-function and C-theorem on affine-Virasoro space

Abstract

An exact C-function which is an action for the Virasoro master equation, is obtained on affine-Virasoro space. The solutions of the master equation are fixed points of an associated flow, which obeys a C-theorem. The closed sub-flow SO( n) diag a flow on the space of graphs and the associated Morse polynomials are known generating functions in graph theory. The general flow also implies a method for prediction of sporadic conformal deformations. We note the resemblance of this system to the expected form of an exact renormalization group equation.