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arXiv 2408.01485hep-thgr-qchep-ph
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红外在壳作用量及其对渐近平直时空中软荷涨落的启示

An Infrared On-Shell Action and its Implications for Soft Charge Fluctuations in Asymptotically Flat Spacetimes

Temple He, Ana-Maria Raclariu, Kathryn M. Zurek

AI总结:

研究了渐近平直时空中 Einstein 引力的红外在壳作用量,证明其等价于软超平移荷、冲击波有效作用量与软有效作用量,并计算软荷量子涨落得出面积定律。

摘要:

我们研究了渐近平直时空中 Einstein 引力的红外在壳作用量,得到了记忆和冲击波时空的有效规范不变边界作用量。我们表明,这两种情况的相空间均由渐近平直时空中的主导软变量参数化,从而将冲击波与软对易子的等价性扩展到了具有非零 Bondi 质量的时空。随后我们证明,我们的在壳作用量等于文献中分别研究过的三个量:(i) 软超平移荷;(ii) 冲击波有效作用量,或等价地即模哈密顿量;以及 (iii) 软有效作用量。最后,我们计算了软超平移荷的量子涨落,并假设超平移参数可被提升为算符,得到了一个面积定律,这与先前表明模哈密顿量具有此类涨落的结果相一致。

英文摘要:

We study the infrared on-shell action of Einstein gravity in asymptotically flat spacetimes, obtaining an effective, gauge-invariant boundary action for memory and shockwave spacetimes. We show that the phase space is in both cases parameterized by the leading soft variables in asymptotically flat spacetimes, thereby extending the equivalence between shockwave and soft commutators to spacetimes with non-vanishing Bondi mass. We then demonstrate that our on-shell action is equal to three quantities studied separately in the literature: $(i)$ the soft supertranslation charge; $(ii)$ the shockwave effective action, or equivalently the modular Hamiltonian; and $(iii)$ the soft effective action. Finally, we compute the quantum fluctuations in the soft supertranslation charge and, assuming the supertranslation parameter may be promoted to an operator, we obtain an area law, consistent with earlier results showing that the modular Hamiltonian has such fluctuations.

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