Broken current anomalous dimensions, conformal manifolds and RG flows

Abstract

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. Holography is instrumental, instead, for computing current anomalous dimensions in $\beta$-deformed superconformal field theories, and in a class of supersymmetric RG flows at large $N$.

21 pages + Appendices. v4: β-function eq. in appendix C corrected, and corresponding fixed point analysis for the O(N) model amended

References in corpus (6)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Exactly marginal deformations from exceptional generalised geometry
• Anomalous dimensions of leading twist conformal operators
• On Conformal Deformations II
• The Epsilon-Expansion from Conformal Field Theory
• The Conformal Manifold of Chern-Simons Matter Theories

Cited by in corpus (6)

• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Notes on Spinning Operators in Fermionic CFT
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• On Higher-Spin Points and Infinite Distances in Conformal Manifolds
• Anomalous dimensions of spinning operators from conformal symmetry
• CFTs on curved spaces