  We consider deformations of CFTs from the perspective of parallel transport
in moduli space. In particular, we show how the deformations of individual
operators can be computed and we also explore how these ideas can be extended
to more general QFTs lacking conformal symmetry. We explore how to write one
theory in terms of operators defined in a nearby theory, related to the first
by a parallel transport in theory space. Using this construction, we describe
how T-duality can be realised and how this provides a different perspective
from the usual Buscher construction.
