The Euclidean on-shell action for linear-dilaton three-dimensional string backgrounds yields a spacetime mass whose square-root form matches the TT-deformed CFT energy formula.
Asymptotically Plane Wave Spacetimes and their Actions
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abstract
We propose a definition of asymptotically plane wave spacetimes in vacuum gravity in terms of the asymptotic falloff of the metric, and discuss the relation to previously constructed exact solutions. We construct a well-behaved action principle for such spacetimes, using the formalism developed by Mann and Marolf. We show that this action is finite on-shell and that the variational principle is well-defined for solutions of vacuum gravity satisfying our asymptotically plane wave falloff conditions.
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The On-shell Gravity Action and Linear Dilaton Holography
The Euclidean on-shell action for linear-dilaton three-dimensional string backgrounds yields a spacetime mass whose square-root form matches the TT-deformed CFT energy formula.