Anomalous Dimensions of Non-Chiral Operators from AdS/CFT

TL;DR

This paper introduces a new Hamiltonian-based method to compute anomalous dimensions of non-chiral operators in N=1 SCFTs with weakly-coupled AdS duals, simplifying previous techniques and enabling new model building possibilities.

Contribution

It develops a novel Hamiltonian approach to directly calculate anomalous dimensions as bound state energies in AdS/CFT, simplifying prior methods based on four-point functions.

Findings

The method simplifies anomalous dimension calculations.

Binding energies in AdS can be positive or negative.

Potential for UV-complete models with positive anomalous dimensions.

Abstract

Non-chiral operators with positive anomalous dimensions can have interesting applications to supersymmetric model building. Motivated by this, we develop a new method for obtaining the anomalous dimensions of non-chiral double-trace operators in N=1 superconformal field theories (SCFTs) with weakly-coupled AdS duals. Via the Hamiltonian formulation of AdS/CFT, we show how to directly compute the anomalous dimension as a bound state energy in the gravity dual. This simplifies previous approaches based on the four-point function and the OPE. We apply our method to a class of effective AdS5 supergravity models, and we find that the binding energy can have either sign. If such models can be UV completed, they will provide the first calculable examples of SCFTs with positive anomalous dimensions.