Finite deformations of conformal field theories using analytically regularized connections

Abstract

We study some natural connections on spaces of conformal field theories using an analytical regularization method. The connections are based on marginal conformal field theory deformations.We show that the analytical regularization preserves conformal invariance and leads to integrability of the marginal deformations. The connections are shown to be flat and to generate well-defined finite parallel transport. These finite parallel transports yield formulations of the deformed theories in the state space of an undeformed theory. The restrictions of the connections to the tangent space are curved but free of torsion.

New moduli spaces from string background independence consistency conditions

“…[ 2,3] brought into the open an operator K which acting on a Riemann surface adds one special puncture throughout the surface minus the unit disks around the punctures (the disks that define the local coordinates around the punctures). This operation is intimately related, at the level of spaces of conformal theories, to the operation of covariant differentiation using a particular connection [ 13,14,15,16,17]. In addition to the operator K, a new family of moduli spaces of Riemann surfaces was introduced, spaces where the surfaces have one special puncture in addition to the ordinary punctures.…”