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arXiv · 2508.10998

The On-shell Gravity Action and Linear Dilaton Holography

Andrea Dei·Kiarash Naderi·Savdeep Sethi
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Abstract

Computing the Euclidean spacetime action on-shell provides a useful way of both testing holographic proposals and determining the string theory sphere partition function. We consider families of three-dimensional linear dilaton spacetimes for which there are holographic proposals that share features of a $T\overline{T}$-deformed CFT. We extend the holographic renormalization program beyond AdS to this class of geometries by identifying the boundary terms needed for a well-defined variational principle and a finite on-shell action. We show that the spacetime energy or mass determined from the on-shell action matches the $T\overline{T}$-deformed two-dimensional CFT energy. This provides more evidence for the role of the $T\overline{T}$ deformation in this holographic correspondence.

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Andrea Dei, Kiarash Naderi, Savdeep Sethi. 2025-08-14. The On-shell Gravity Action and Linear Dilaton Holography. https://arxiv.org/abs/2508.10998

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