Broken current anomalous dimensions, conformal manifolds and RG flows

TL;DR

This paper explores how conformal symmetry constrains anomalous dimensions of broken currents in deformed conformal field theories, using both field theory and holographic methods across various models.

Contribution

It provides a unified approach to compute broken current anomalous dimensions in diverse conformal field theory deformations, including holographic and field-theoretic cases.

Findings

Computed anomalous dimensions in $O(N)$ models in $d=4- ext{epsilon}$ dimensions.

Used holography to analyze $eta$-deformed superconformal theories.

Analyzed supersymmetric RG flows at large $N$.

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 $N$.