DEFORMATIONS IN CLOSED STRING THEORY - CANONICAL FORMULATION AND REGULARIZATION

We study deformations of closed string theory by primary fields of con formal weight (1, 1), using conformal techniques on the complex plane. A canonical surface integral formalism for computing commutators in a non-holomorphic theory is constructed, and explicit formulae for defo rmations of operators are given. We identify the unique regularization of the arising divergences that respects conformal invariance, and co nsider the corresponding parallel transport. The associated connection is metric compatible and carries no curvature.