Abstract The deformation, built from the components of the stress tensor and of a 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 -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 -deformed CFTs can be obtained from field-dependent coordinate transformations.
It has been recently shown that the deformation of an arbitrary two-dimensional conformal field theory by the composite irrelevant operator T \bar T T T ‾ , built from the components of the stress tensor, is solvable; in particular, the finite-size spectrum of the deformed theory can be obtained from that of the original CFT through a universal formula. We study a similarly universal, Lorentz-breaking deformation of two-dimensional CFTs that possess a conserved U(1) U ( 1 ) current, J J . The deformation takes the schematic form J \bar T J T ‾ and is interesting because it preserves an SL(2,\mathbb{R}) \times U(1) S L ( 2 , ℝ ) × U ( 1 ) subgroup of the original global conformal symmetries. For the case of a purely (anti)chiral current, we find the finite-size spectrum of the deformed theory and study its thermodynamic properties. We test our predictions in a simple example involving deformed free fermions.
We derive universal constraints on
(1+1)d rational conformal field theories (CFTs) that can arise as transitions between topological theories protected by a global symmetry. The deformation away from criticality to the trivially gapped phase is driven by a symmetry preserving relevant deformation and under renormalization group flow defines a conformal boundary condition of the CFT. When a CFT can make a transition between distinct trivially gapped phases the spectrum of the CFT quantized on an interval with the associated boundary conditions has degeneracies at each energy level. Using techniques from boundary CFT and modular invariance, we derive universal inequalities on all such degeneracies, including those of the ground state. This establishes a symmetry enriched
c-theorem, effectively a lower bound on the central charge which is strictly positive, for this class of CFTs and symmetry protected flows. We illustrate our results for the case of flows protected by
SU(M)/ZM symmetry. In this case, all SPT transitions can arise from the WZW model
SU(M)1, and we develop a dictionary between conformal boundary conditions and relevant operators.