Abstract
We propose a symmetry of TT¯ deformed 2D CFT, which preserves the trace relation. The deformed conformal killing equation is obtained. Once we consider the background metric runs with the deformation parameter μ, the deformation contributes an additional term in conformal killing equation, which plays the role of renormalization group flow of metric. The conformal symmetry coincides with the fixed point. On the gravity side, this deformed conformal killing equation can be described by a new boundary condition of AdS3. In addition, based on the deformed conformal killing equation, we derive that the stress tensor of the deformed CFT equals to Brown-York's quasilocal stress tensor on a finite boundary with a counterterm. For a specific example, BTZ black hole, we get TT¯ deformed conformal killing vectors and the associated conserved charges are also studied.
Highlights
The deformation in general dimensions are considered [5, 6]
According to the flow equation of metric, we find the deformation effect can be expressed by adding a change rate of metric along parameter μ term on the conformal killing equation, and conformal symmetry coincides with the fixed point
The purpose of this paper is to explore the symmetry of T Tdeformed CFT
Summary
We review some main results about T Tdeformed CFT and its holographic aspects, which would be useful for discussing the symmetry in this paper. The trace relation is just the generalization of traceless of a CFT along the T Tflow This will lead to a variation of path integral by inserting a factor e−δS. Above equation can be expressed as hij = δgij = 2δμ(gijT − Tij) This means that the background metric runs with the parameter μ. I.e. μ = 0, is a 2D CFT, this result holds for a small μ or large c limit, which means c is large enough but fix the μc This conclusion was obtained by Cardy via the viewpoint of random geometry [19], and the correlation function has been calculated [14, 20].
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