Root-T T Deformed Boundary Conditions in Holography
Abstract
We develop the holographic dictionary for pure AdS3 gravity where the Lagrangian of the dual 2d conformal field theory has been deformed by an arbitrary function of the energy-momentum tensor. In addition to the T T deformation, examples of such functions include a class of marginal stress tensor deformations which are special because they leave the generating functional of connected correlators unchanged up to a redefinition of the source and expectation value. Within this marginal class, we identify the unique deformation that commutes with the T T flow, which is the root-T T operator, and write down the modified boundary conditions corresponding to this root-T T deformation. We also identify the unique marginal stress tensor flow for the cylinder spectrum of the dual CFT which commutes with the inviscid Burgers' flow driven by T T, and we propose this unique flow as a candidate root-T T deformation of the energy levels. We study BTZ black holes in AdS3 subject to root-T T deformed boundary conditions, and find that their masses flow in a way which is identical to that of our candidate root-T T energy flow equation, which offers evidence that this flow is the correct one. Finally, we also obtain the root-T T deformed boundary conditions for the gauge field in the Chern-Simons formulation of AdS3 gravity.
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