经典统计Yang-Mills模拟揭示实时量子引力动力学的相变与振荡特性

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本文主要探讨了实时量子重力动力学在经典统计SU(N) Yang-Mills理论中的应用。研究人员使用带有八个标量的圆周上的晶格模拟方法，对这一理论进行了深入研究。SU(N) Yang-Mills理论是一种描述强相互作用的重要数学模型，在量子场论中扮演着核心角色，尤其是在与引力理论的某些方面寻找量子化版本时。在实验中，通过对空间Wilson环的特征值分布进行测量，研究者发现了两种不同的相位，这些相位被认为与双引力图中的黑洞和黑弦相态相对应。这种区分基于系统的总能量和圆周半径，这体现了理论在不同能量尺度下的物理特性变化。相变过程可能反映了理论中潜在的拓扑结构转变，这在双引力理论中对应于黑洞和黑弦之间的转换。研究者通过实施“淬火”实验，即先让系统处于一个特定相位，然后快速改变总能量，观察系统的实时响应。他们观察到系统在经历特征阻尼振荡后，能够迅速地从原平衡状态过渡到新的能量对应的平衡状态。这种阻尼振荡被解释为黑洞或黑弦状态向最终稳定状态的准正态振铃，表明即使在考虑α'（引力理论中的修正项）的影响下，拓扑变化相关的奇异性问题得到了一定程度的缓解。此外，作者还分析了系统最低层次的准准模式的实部和虚部，这些数据对于理解理论的动态行为和可能的物理意义至关重要。他们通过测量和解析这些模式，能够更深入地揭示量子重力动力学的微观行为及其与经典统计模拟的关联。这篇研究通过数值模拟提供了一个实时光谱学的视角，展示了经典统计Yang-Mills理论如何与量子重力理论中的基本概念如黑洞和黑弦相联系，并且对理论的稳定性及修正项的作用进行了初步探索。这项工作不仅有助于深化对量子重力的理解，也为未来的研究提供了宝贵的实验证据和理论基础。

JHEP01(2019)201

Figure 2. Conjectured equilibrium phase diagram for the gravity dual to 2d maximal SYM (left)

and purely bosonic Yang-Mills with 8 scalars (right) as a function of the length of the spatial (r

)

and temporal (β, inverse temperature) circles, respectively. The arrow on the r.h.s. panel indicates

applicability of numerical simulations in this work.

From a gauge theory perspective, the real-time dynamics of fully quantum 2d SYM

is expected to be well approximated by its classical dynamics for modes which are highly

occupied. For bosons in equilibrium, this is the case for the modes with energy ω obeying

βω  1, or the low-energy modes. At small temporal circle radius β or high temperature,

many bosonic modes can be well approximated by their classical dynamics. Additionally,

at high temperature fermionic modes develop a large thermal mass, so they can be expected

to decouple and thus not contribute to observables that are insensitive to the number of

degrees of freedom of the theory. Thus at high temperature, one can expect the dynamics

of 2d SYM to be at least qualitatively well approximated by the classical dynamics of

purely bosonic Yang-Mills theory. This expectation has indeed be conﬁrmed in previous

numerical studies in other dimensions [40–44] and a comparison of Monte Carlo results

between 2d SYM and 2d SU(N) pure gauge theory [11]. (Note that generalizations of the

classical statistical framework to include quantum eﬀects to some extent may be possible,

cf. [45–48].)

Not surprisingly, some aspects of the 2d SYM dynamics cannot be captured by the

purely bosonic classical statistical approximation. For instance, by neglecting the fermions

one is studying the phase diagram of the purely bosonic theory shown in ﬁgure 2, cf.

refs. [5, 11, 49, 50]. However, at high temperature, the 2d SYM and pure Yang-Mills phase

diagrams become indistinguishable, such that the classical statistical simulations performed

as part of this work could reasonably be expected to oﬀer qualitative insights into the black

string phase, and potentially also the deconﬁned black hole phase.

From string theory point of view, the high temperature (weak coupling) regime should

describe a highly stringy system, where the α

corrections are large but one can still tune

the g

correction by dialing N. By performing direct numerical simulations of the high

temperature gauge theory dynamics, one can study whether the α

correction is suﬃcient

– 3 –

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