Linearization (in)stabilities and crossed products

IF 5.4 1区 物理与天体物理 Q1 Physics and Astronomy
Julian De Vuyst, Stefan Eccles, Philipp A. Höhn, Josh Kirklin
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引用次数: 0

Abstract

Modular crossed product algebras have recently assumed an important role in perturbative quantum gravity as they lead to an intrinsic regularization of entanglement entropies by introducing quantum reference frames (QRFs) in place of explicit regulators. This is achieved by imposing certain boost constraints on gravitons, QRFs and other fields. Here, we revisit the question of how these constraints should be understood through the lens of perturbation theory and particularly the study of linearization (in)stabilities, exploring when linearized solutions can be integrated to exact ones. Our aim is to provide some clarity about the status of justification, under various conditions, for imposing such constraints on the linearized theory in the GN → 0 limit as they turn out to be of second-order. While for spatially closed spacetimes there is an essentially unambiguous justification, in the presence of boundaries or the absence of isometries this depends on whether one is also interested in second-order observables. Linearization (in)stabilities occur in any gauge-covariant field theory with non-linear equations and to address this in a unified framework, we translate the subject from the usual canonical formulation into a systematic covariant phase space language. This overcomes theory-specific arguments, exhibiting the universal structure behind (in)stabilities, and permits us to cover arbitrary generally covariant theories. We comment on the relation to modular flow and illustrate our findings in several gravity and gauge theory examples.

线性化(in)稳定性和交叉积
模交叉积代数最近在微扰量子引力中扮演了重要的角色,因为它们通过引入量子参考框架(QRFs)来代替显式调节器,从而导致纠缠熵的内在正则化。这是通过对重子、qrf和其他场施加一定的推进约束来实现的。在这里,我们重新审视这些约束应该如何通过摄动理论的镜头来理解的问题,特别是线性化(in)稳定性的研究,探索线性化解何时可以集成到精确解。我们的目的是提供一些澄清的状态,在各种条件下,对GN→0极限下的线性化理论施加这样的约束,因为它们是二阶的。虽然对于空间封闭的时空有一个本质上明确的理由,但在存在边界或不存在等距时,这取决于人们是否也对二阶可观测值感兴趣。线性化(in)稳定性发生在任何具有非线性方程的规范协变场论中,为了在统一的框架中解决这个问题,我们将主题从通常的规范公式转换为系统的协变相空间语言。这克服了理论特定的论点,展示了稳定性背后的普遍结构,并允许我们涵盖任意的一般协变理论。我们评论了与模流的关系,并在几个重力和规范理论的例子中说明了我们的发现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of High Energy Physics
Journal of High Energy Physics 物理-物理:粒子与场物理
CiteScore
10.30
自引率
46.30%
发文量
2107
审稿时长
1.5 months
期刊介绍: The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal. Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles. JHEP presently encompasses the following areas of theoretical and experimental physics: Collider Physics Underground and Large Array Physics Quantum Field Theory Gauge Field Theories Symmetries String and Brane Theory General Relativity and Gravitation Supersymmetry Mathematical Methods of Physics Mostly Solvable Models Astroparticles Statistical Field Theories Mostly Weak Interactions Mostly Strong Interactions Quantum Field Theory (phenomenology) Strings and Branes Phenomenological Aspects of Supersymmetry Mostly Strong Interactions (phenomenology).
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