  The $J\bar T$ deformation, built from the components of the stress tensor and
of a $U(1)$ current, is a universal irrelevant deformation of two-dimensional
CFTs that preserves the left-moving conformal symmetry, while breaking locality
on the right-moving side. Operators in the $J\bar T$-deformed CFT are naturally
labeled by the left-moving position and right-moving momentum and transform in
representations of the one-dimensional extended conformal group. We derive an
all-orders formula for the spectrum of conformal dimensions and charges of the
deformed CFT, which we cross-check at leading order using conformal
perturbation theory. We also compute the linear corrections to the
one-dimensional OPE coefficients and comment on the extent to which the
correlation functions in $J\bar T$-deformed CFTs can be obtained from
field-dependent coordinate transformations.
