Induced 4D self-dual quantum gravity: W algebraic approach

Abstract

The authors consider the functional integral quantization of the equation which describes a development of cross sections in a twistor space corresponding to self-dual gravity. At the classical level the system permits a local area-preserving diffeomorphism as its symmetry. Assuming Winfinity algebra at the quantized level, they derive an effective action for this equation via the coadjoint orbit method. The result consists of an infinite sum of two-dimensional effective Lagrangians including infinitesimal Polyakov two-dimensional (light-cone gauge) gravity as its first term. The higher order terms are the result of the central extensions of Winfinity algebra associated with higher conformal-spin operators.