Broken current anomalous dimensions, conformal manifolds and RG flows

Understand

We consider deformations of a conformal field theory that explicitly break some global symmetries of the theory.

• If the deformed theory is still a conformal field theory, one can exploit the constraints put by conformal symmetry to compute broken currents anomalous dimensions.
• We consider several instances of this scenario, using field theory techniques and also holographic ones, where necessary.
• Field theoretical methods suffice to discuss examples of symmetry-breaking deformations of the $O(N )$ model in $d=4-\epsilon$ dimensions.