A regulated large-spin effective Hamiltonian with three-body phi exchange and local terms gives the O(lambda^2) anomalous dimension of [Phi, Phi^2]_J, including a log J / J^(2 Delta) correction.
Anomalous Dimensions of Non-Chiral Operators from AdS/CFT
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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.
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Towards Large-Spin Effective Theory I: Three-Particle States in AdS $\phi^4$ Theory
A regulated large-spin effective Hamiltonian with three-body phi exchange and local terms gives the O(lambda^2) anomalous dimension of [Phi, Phi^2]_J, including a log J / J^(2 Delta) correction.