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Generalised global symmetries in states with dynamical defects: the case of the transverse sound in field theory and holography

机译:具有动态缺陷的状态的广义全局对称性:案例   场论和全息术中的横向声音

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摘要

In this work, we show how states with conserved numbers of dynamical defects(strings, domain walls, etc.) can be understood as possessing generalisedglobal symmetries even when the microscopic origins of these symmetries areunknown. Using this philosophy, we build an effective theory of a$2+1$-dimensional fluid state with two perpendicular sets of immersed elasticline defects. When the number of defects is independently conserved in eachset, then the state possesses two one-form symmetries. Normally, suchviscoelastic states are described as fluids coupled to Goldstone bosonsassociated with spontaneous breaking of translational symmetry caused by theunderlying microscopic structure-the principle feature of which is a transversesound mode. At the linear, non-dissipative level, we verify that our theory,based entirely on symmetry principles, is equivalent to a viscoelastic theory.We then build a simple holographic dual of such a state containing dynamicalgravity and two two-form gauge fields, and use it to study its hydrodynamic andhigher-energy spectral properties characterised by non-hydrodynamic, gappedmodes. Based on the holographic analysis of transverse two-point functions, westudy consistency between low-energy predictions of the bulk theory and theeffective boundary theory. Various new features of the holographic dictionaryare explained in theories with higher-form symmetries, such as themixed-boundary-condition modification of the quasinormal mode prescription thatdepends on the running coupling of the boundary double-trace deformations.Furthermore, we examine details of low- and high-energy parts of the spectrumthat depend on temperature, line defect densities and the renormalisation groupscale (dimensional transmutation).
机译:在这项工作中,我们展示了即使在动力学对称缺陷的微观起源未知的情况下,具有动态缺陷(字符串,畴壁等)数量守恒的状态也可以理解为具有广义全局对称性。使用这种原理,我们建立了一个有效的2 +1维维流体状态理论,其中包含两组垂直的浸入式弹性线缺陷。当缺陷数量在每组中独立保存时,则该状态具有两个单一形式的对称性。通常,这种粘弹性状态被描述为耦合至金石玻色子的流体,并伴随着由下层微观结构引起的平移对称性的自发破坏,其微观特征主要是横向声波模式。在线性,非耗散级别上,我们验证了我们的理论完全基于对称原理,等效于粘弹性理论,然后构建了一个包含动态重力和两个两个形式规范场的状态的简单全息对偶。用它来研究其水动力和高能谱特性,其特征在于非水动力,缺口模式。基于横向两点函数的全息分析,整体理论的低能预测与有效边界理论之间的西律一致性。全息辞典的各种新功能在具有较高形式对称性的理论中得到了解释,例如准标准模态处方的混合边界条件修改(取决于边界双迹线变形的运行耦合)。以及依赖于温度,线缺陷密度和重新归一化族尺度(尺寸trans变)的光谱高能部分。

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