标题： 低维引力中的守恒性和可积性 显示英文标题

标题： Conservation and Integrability in Lower-Dimensional Gravity

摘要： 我们研究了在无穷远处二维和三维引力理论中的电荷守恒和可积性问题。 分析是在一个框架内进行的，该框架允许我们同时处理渐近局部AdS和渐近局部平直时空。 在二维情况下，我们从一个包含JT和CGHS标量引力理论的一般模型类开始，而在三维情况下，我们在爱因斯坦引力中进行研究。 在两种情况下，我们构建了相空间，并通过全息重整化程序对辛结构中出现的发散进行正则化。 我们表明电荷表达式通常是有限的，但不守恒，可以通过对渐近对称参数的场依赖重定义使其可积。 显示英文摘要

摘要： We address the questions of conservation and integrability of the charges in two and three-dimensional gravity theories at infinity. The analysis is performed in a framework that allows us to treat simultaneously asymptotically locally AdS and asymptotically locally flat spacetimes. In two dimensions, we start from a general class of models that includes JT and CGHS dilaton gravity theories, while in three dimensions, we work in Einstein gravity. In both cases, we construct the phase space and renormalize the divergences arising in the symplectic structure through a holographic renormalization procedure. We show that the charge expressions are generically finite, not conserved but can be made integrable by a field-dependent redefinition of the asymptotic symmetry parameters.