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arXiv · 2407.18866

A Comment on Deriving the Gibbons-Hawking-York Term From the String Worldsheet

Amr Ahmadain·Vasudev Shyam·Zihan Yan
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Abstract

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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Amr Ahmadain, Vasudev Shyam, Zihan Yan. 2024-07-26. A Comment on Deriving the Gibbons-Hawking-York Term From the String Worldsheet. https://arxiv.org/abs/2407.18866

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