红外发散的变分方法：在黑洞作用量积分和全息威尔逊圈中的应用
The variational approach to infrared divergencies: Applications to black hole action integrals and holographic Wilson loops
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中文总结 AI 辅助
研究利用对壳上作用量变分进行重整化的方法，该方法具通用形式且能自然解释为泛函空间上的1-形式，借此给出清晰重整化处方。将此用于黑洞作用量及全息威尔逊圈计算，结果与标准结果尤其是全息重整化一致。
中文摘要 AI 辅助
对壳上作用量变分进行重整化比直接重整化作用量本身有两个重要优势。其一，作用量的变分具有通用形式，其中体贡献恒为零，重整化问题自动定域在边界，无需体减法。其二，作用量的变分可自然解释为泛函空间上的1-形式，精确与非精确1-形式的区别给出清晰的重整化处方。我们将这些想法应用于壳上黑洞作用量的计算，给出通用算法并讨论了克尔 - 纽曼等黑洞的例子，还将同样技术用于全息威尔逊圈的计算，所有结果与标准结果一致，特别是与全息重整化一致。
英文摘要
Renormalizing the on-shell action variation offers two important advantages over renormalizing the action itself. First, the variation of the action has a universal form in which the bulk contribution vanishes identically. As a result, the renormalization problem is automatically localized at the boundary; no bulk subtractions are required. Second, the variation of the action admits a natural interpretation as a 1-form on functional space. The distinction between exact and non-exact 1-forms provides a clear renormalization prescription. We apply these ideas to the computation of on-shell black hole actions. After presenting the general algorithm, we discuss some examples, including Kerr-Newman, Kerr-Newman-AdS, Taub-NUT, Taub-Bolt, and STU black holes. We also apply the same techniques to the computation of holographic Wilson loops. All results agree with standard results, in particular with holographic renormalization.
