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A Comment on Deriving the Gibbons-Hawking-York Term From the String Worldsheet
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In this note, we show that the noncovariant metric boundary term obtained from the nonlinear sigma model worldsheet derivation of the bulk off-shell sphere partition function is closely related to the Einstein boundary term in the Gamma-Gamma noncovariant action. In fact, when expressed in terms of the trace of the extrinsic curvature tensor, we illustrate that this boundary term has one-half the coefficient of the Gibbons-Hawking-York boundary term required such that the total (bulk plus boundary) off-shell classical action has a well-posed variational principle with Dirichlet boundary conditions.
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Cited by 2 Pith papers
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Boundary terms in string field theory
The free closed string field theory action is supplemented with a boundary term, derived from the failure of BRST cyclicity, that reproduces the Gibbons-Hawking-York term at low energies.
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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.
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