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arXiv 2503.03374hep-thhep-phnucl-th
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耗散中性流体的有效作用量的全息推导

Holographic derivation of effective action for a dissipative neutral fluid

Yanyan Bu, Xiyang Sun

AI总结:

本文利用施温格-凯尔迪什全息处方,通过求解复化AdS黑膜背景中的双狄利克雷问题并采用部分在壳方案,推导出耗散中性流体的边界有效作用量,成功重现经典流体力学结果。

摘要:

利用施温格-凯尔迪什闭合时间路径的全息处方,我们推导出一个耗散中性流体的有效作用量,该流体在渐近AdS时空中由爱因斯坦引力全息描述。在对偶引力的鞍点近似下,通过求解生活在复化静态AdS黑膜背景中的线性化引力场的双狄利克雷问题来实现这一目标。我们采用部分在壳方案求解体动力学,这等价于在边界场论中“积掉”有能隙的模式。流体时空中的边界有效作用量被识别为部分在壳的体作用量,计算到边界导数的一阶和AdS边界数据的三阶。改写回物理时空后,该边界有效作用量成功重现了经典流体力学框架中已知的各种结果,证实了我们的全息推导。

英文摘要:

Using a holographic prescription for the Schwinger-Keldysh closed time path, we derive the effective action for a dissipative neutral fluid holographically described by the Einstein gravity in an asymptotic AdS spacetime. In the saddle point approximation for the dual gravity, the goal is achieved by solving the double Dirichlet problem for the linearized gravitational field living in a complexified static AdS black brane background. We adopt a partially on-shell scheme for solving the bulk dynamics, which is equivalent to ``integrating out'' the gapped modes in the boundary field theory. The boundary effective action in the fluid spacetime, identified as the partially on-shell bulk action, is computed to first order in boundary derivative and to cubic order in AdS boundary data. The boundary effective action, rewritten in the physical spacetime, successfully reproduces various results known in the framework of classical hydrodynamics, confirming our holographic derivation.

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