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$T \bar T$ Deformations, Massive Gravity and Non-Critical Strings · Around

2019

$T \bar T$ Deformations, Massive Gravity and Non-Critical Strings

Tolley, Andrew J.

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The $T \bar T$ deformation of a 2 dimensional field theory living on a curved spacetime is equivalent to coupling the undeformed field theory to 2 dimensional `ghost-free' massive gravity.

We derive the equivalence classically, and using a path integral formulation of the random geometries proposal, which mirrors the holographic bulk cutoff picture.
We emphasize the role of the massive gravity \stu fields which describe the diffeomorphism between the two metrics.
For a general field theory, the dynamics of the \stu fields is non-trivial, however for a CFT it trivializes and becomes equivalent to an additional pair of target space dimensions with associated curved target space geometry and dynamical worldsheet metric.

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