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Partial integration of the Gibbons-Hawking-York boundary term
In https://arxiv.org/abs/1402.6334 on page 16 in their Eq. (5.21), they go from the equation
$$S_G+S_\chi\approx\int d^2x\sqrt{-g}XR+\int dt\sqrt{-\gamma}XK$$
to the equation
$$=\int d^2x \sqrt{-g}\...