标题： 弦世界面的GHY边界项到一次项 显示英文标题

标题： The GHY boundary term from the string worldsheet to linear order

摘要： 利用图像法，我们从球形世界面出发，将爱因斯坦-$\Gamma^2$作用量在半空间中的边界项推导至$\alpha'$的一阶以及平坦半空间附近的度规摄动的线性阶。 超过100年前，爱因斯坦写下这一$\Gamma^2$作用量，它包含一个由Gibbons-Hawking-York作用量以及两个额外项组成的边界项，这些附加项是度规、法向量和切向导数的函数。 通过这个边界项，总的（体+边界）球有效作用量对于狄利克雷边界条件具有适定的变分原理。 显示英文摘要

摘要： 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.