论文标题
在出现的自发性手性对称性破坏的紧急双全息描述中,在IR处流向有效量子力学
Renormalization group flow to effective quantum mechanics at IR in an emergent dual holographic description for spontaneous chiral symmetry breaking
论文作者
论文摘要
通过以非扰动方式实施Wilsonian Renoralization组(RG)转换,我们构建了一个有效的全息双重描述,并以RG量表识别出紧急的引发。采用大$ -n $限制,我们获得了订单参数字段的运动方程,这里是我们明确演示的手性冷凝物。特别是,相互交织的结构在重新归一化耦合函数的一阶RG流程方程与订单参数场的二阶微分方程之间表现出来,因此称为非驾驶RG侵入性RG-屈光平均值均值。假设翻译对称为真空状态,我们基于UV-和IR区域溶液之间的匹配方法求解了这些非线性耦合平均场方程。结果,我们发现从弱耦合的手性对称紫外线固定点到强烈相关的手性对称性损坏的IR固定点的RG流动,在IR中,Dirac Fermions重新归一化的速度最快,有效的量子力学消失了。此外,我们将耦合函数的这些RG流转换为新兴度量张量的函数,并提取从UV和IR区域溶液中构建的新兴全息时空的几何特性。令人惊讶的是,我们在ryu-takayanagi公式中获得了纠缠熵的体积定律,这意味着即使在零温度下,也可以在无限截止的极限中出现黑洞型溶液。我们批判性地讨论了该解决方案的领域理论解释,以潜在的无缘多粒子激发光谱。
Implementing the Wilsonian renormalization group (RG) transformation in a nonperturbative way, we construct an effective holographic dual description with an emergent extradimension identified with an RG scale. Taking the large$-N$ limit, we obtain an equation of motion of an order-parameter field, here the chiral condensate for our explicit demonstration. In particular, an intertwined structure manifests between the first-order RG flow equations of renormalized coupling functions and the second-order differential equation of the order-parameter field, thus referred to as a nonperturbative RG-improved mean-field theory. Assuming translational symmetry as a vacuum state, we solve these nonlinear coupled mean-field equations based on a matching method between UV- and IR-regional solutions. As a result, we find an RG flow from a weakly-coupled chiral-symmetric UV fixed point to a strongly-correlated chiral-symmetry broken IR fixed point, where the renormalized velocity of Dirac fermions vanishes most rapidly and effective quantum mechanics appears at IR. Furthermore, we translate these RG flows of coupling functions into those of emergent metric tensors and extract out geometrical properties of the emergent holographic spacetime constructed from the UV- and IR-regional solutions. Surprisingly, we obtain the volume law of entanglement entropy in the Ryu-Takayanagi formula, which implies appearance of a black hole type solution in the limit of infinite cutoff even at zero temperature. We critically discuss our field theoretic interpretation for this solution in terms of potentially gapless multi-particle excitation spectra.