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arXiv · 2411.06400

The GHY boundary term from the string worldsheet to linear order

Amr Ahmadain·Shoaib Akhtar·Rifath Khan
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Abstract

Using the method of images we derive the boundary term of the Einstein-$\Gamma^2$ action in half-space from the spherical worldsheet to first order in $\alpha'$ and to linear order in the metric perturbation around flat half-space. The $\Gamma^2$ action, written down by Einstein more than 100 years ago, includes a boundary term that consists of the Gibbons-Hawking-York action along with two additional terms that are functions of the metric, normal vector, and tangential derivatives. With this boundary term, the total (bulk + boundary) sphere effective action has a well-posed variational principle for Dirichlet boundary conditions.

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Amr Ahmadain, Shoaib Akhtar, Rifath Khan. 2024-11-10. The GHY boundary term from the string worldsheet to linear order. https://arxiv.org/abs/2411.06400

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