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arXiv 2601.04321hep-th
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反德西特空间中的着装与筛选

Dressing and Screening in Anti-de Sitter

Dipartimento di Fisica, Università di Trieste(的里雅斯特大学物理系);INFN, Sezione di Trieste(意大利国家核物理研究所的里雅斯特分部);Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences(中国科学院大学卡弗里理论科学研究所);Laboratory for Theoretical Fundamental Physics, Institute of Physics, Ecole Polytechnique Fédérale de Lausanne(洛桑联邦理工学院物理研究所基础物理实验室);CERN, Theoretical Physics Department(欧洲核子研究中心理论物理部)

Ankur, Lorenzo Di Pietro, Victor Gorbenko, Shota Komatsu, Veronica Sacchi

AI总结:

研究AdS空间中带电标量与光子的非标准Higgs机制及更高形式对称性自发破缺的物理影响。

摘要:

受定义规范不变可观测量问题的启发,并考虑到德西特(dS)和反德西特(AdS)空间中扰动理论的紧密联系,我们研究了AdS空间中的标量电磁动力学,这些研究场景大多未被探索但对dS物理相关。对于具有标准(狄利克雷)边界条件的光子,我们分析了具有破坏U(1)对称性的边界条件的带电标量。这导致了一种非标准的Higgs机制,在其中规范场在无经典真空期望值的情况下获得一阶环状质量。利用AdS中扰动理论的最新进展,我们明确计算了这种质量并评估了带电标量四点函数。我们还提供了一种基于边界瓦尔德恒等式替代推导的方法。对于具有替代(Neumann)边界条件的光子,其中局部带电算符不规范不变,我们通过将带电场着装为测地线威尔逊线来构造物理可观测量。这些着装算符具有良好的共形性质,并且不物理的光子模式从其相关函数中分离。显式的一阶计算进一步揭示了边界场强的分离,我们为此提供了一个基于更高形式对称性的非微扰论证。在过程中,我们解释了AdS中自发打破更高形式对称性的物理后果,包括倾斜算子的作用,一形式对称性与边界威尔逊线端点的关系,以及保守电流对bulk规范场的广义对称性解释。

英文摘要:

Motivated by a question of defining gauge-invariant observables in cosmology and by the close connection between perturbation theory in de Sitter (dS) and Anti-de Sitter (AdS), we study scalar electrodynamics in AdS in setups that are largely unexplored but relevant for dS physics. For photons with standard (Dirichlet) boundary conditions, we analyze charged scalars whose boundary conditions break the $U(1)$ symmetry. This leads to a nonstandard Higgs mechanism in which the gauge field acquires a one-loop mass without a classical vacuum expectation value. Using recent advances in perturbation theory in AdS, we compute this mass explicitly and evaluate charged-scalar four-point functions. We also provide an alternative derivation based on boundary Ward identities. For photons with alternate (Neumann) boundary conditions, where local charged operators are not gauge invariant, we construct physical observables by dressing charged fields with geodesic Wilson lines. These dressed operators have well-behaved conformal properties and unphysical photon modes decouple from their correlation functions. Explicit one-loop computations further reveal the decoupling of boundary field strengths, for which we provide a nonperturbative argument based on higher-form symmetry. Along the way, we explain the physical consequences of spontaneous breaking of higher-form symmetry in AdS, including the role of the tilt operator, the relation between one-form symmetry and endpoints of Wilson lines at the boundary, and a generalized-symmetry interpretation of conserved currents dual to bulk gauge fields.

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