UCLA

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 TT¯ 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 TT¯ flow, which is the root-TT¯ operator, and write down the modified boundary conditions corresponding to this root-TT¯ 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 TT¯, and we propose this unique flow as a candidate root-TT¯ deformation of the energy levels. We study BTZ black holes in AdS3 subject to root-TT¯ deformed boundary conditions, and find that their masses flow in a way which is identical to that of our candidate root-TT¯ energy flow equation, which offers evidence that this flow is the correct one. Finally, we also obtain the root-TT¯ deformed boundary conditions for the gauge field in the Chern-Simons formulation of AdS3 gravity.