Nonequilibrium thermodynamics perspectives for the monotonicity of the renormalization group flow
Nonequilibrium thermodynamics perspectives for the monotonicity of the renormalization group flow
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DOI：
10.1103/physrevd.108.126022
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发表时间：
2023-10
影响因子：
5
通讯作者：
Ki-Seok Kim;Shinsei Ryu
中科院分区：
文献类型：
--
作者：
Ki-Seok Kim;Shinsei Ryu
从非平衡态热力学的角度研究了重整化群（RG）流的单调性。将Martin-Siggia-Rose形式主义应用于wilson RG变换，我们将RG流动方程明显地纳入有效作用中，其中所有耦合函数都是动态提升的。结果，我们得到了一个涌现全息对偶有效场论，其中一个额外的维度出现在威尔逊RG变换中。研究发现，BRST型变换在整体有效作用中起着重要作用，并给出了重归一化耦合场间相关函数的Ward恒等式。由于半经典非平衡动力学中的广义涨落耗散定理可以从这类BRST对称的Ward恒等式中理解，我们发现RG流在全息对偶有效场论中的原理本质上是相同的。此外，我们讨论了这些“非平衡功恒等式”如何与RG流的单调性相关，例如，c定理。特别地，我们引入了动态耦合场的熵泛函，并证明了总熵泛函的产率总是正的，表明RG流的不可逆性。
We investigate the monotonicity of the renormalization group (RG) flow from the perspectives of nonequilibrium thermodynamics. Applying the Martin-Siggia-Rose formalism to the Wilsonian RG transformation, we incorporate the RG flow equations manifestly in an effective action, where all coupling functions are dynamically promoted. As a result, we obtain an emergent holographic dual effective field theory, where an extra dimension appears from the Wilsonian RG transformation. We observe that Becchi-Rouet-Stora-Tyutin (BRST)-type transformations play an important role in the bulk effective action, which give rise to novel Ward identities for correlation functions between the renormalized coupling fields. As generalized fluctuation-dissipation theorems in the semiclassical nonequilibrium dynamics can be understood from the Ward identities of such BRST symmetries, we find essentially the same principle for the RG flow in the holographic dual effective field theory. Furthermore, we discuss how these ``nonequilibrium work identities"can be related to the monotonicity of the RG flow, for example, the $c-theorem$. In particular, we introduce an entropy functional for the dynamical coupling field and show that the production rate of the total entropy functional is always positive, indicating the irreversibility of the RG flow.