Very special T(J)over-bar deformed CFT

We study a very special class of T (J) over bar deformations of conformal field theories in two dimensions. While the deformations break the Lorentz symmetry, they preserve the twisted Lorentz symmetry. The resulting theory has right-moving Virasoro as well as left-moving translation and left-moving (chiral) scale symmetry without left-moving special conformal symmetry (nor left-moving Virasoro symmetry). As in the original T (J) over bar deformations, they may be regarded as an operator dependent nonlocal change of coordinates. We show concrete examples based on world sheet string theory and discuss how the nonunitary nature enables us to circumvent various no-go theorems.