Scholarlink

<p>We consider a free complex massive scalar on the quotient spacetime AdS<sub>3</sub><i>/</i>ℤ, which has the isometry group SO(2, 2) rather than its universal cover. This problem is of interest as a special example of QFT on a spacetime with closed timelike curves (CTCs), as a new context in which to study generalizations of AdS/CFT and for its role in celestial holography. A basis of time-periodic solutions to the Klein-Gordon wave equation is found in terms of hypergeometric functions. They fall into a PT even and a PT odd principal series representation, rather than the more familiar highest-weight representations of the cover of SO(2, 2). For masses below the Breitenlohner-Freedman (BF) bound, the modes fall on the unitary principal series. The presence of CTCs precludes the usual canonical quantization, but geometric quantization, which begins with a symplectic form on the phase space of classical solutions, is applicable. Operators, commutators, an SO(2, 2) invariant vacuum and a Fock space are constructed and transform like those of a CFT<sub>2</sub>. The Fock space norm is positive below the BF bound. In celestial holography, AdS<sub>3</sub><i>/</i>ℤ arises as leaves of a hyperbolic foliation of Klein space. Our analysis determines new entries in the symmetry-constrained celestial bulk-to-boundary dictionary. In particular the Klein space 𝒮-matrix is dual to a maximally entangled state in the tensor product of two copies of the ‘wedge CFT<sub>2</sub>’ associated to the timelike and spacelike wedges of Klein space. Translation invariance is not present in the wedge CFT<sub>2</sub> itself but emerges as a property of this maximally entangled state.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Quantum fields on time-periodic AdS3/ℤ

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月1日

查看全文
  • Walker Melton,
  • Andrew Strominger,
  • Tianli Wang

摘要

We consider a free complex massive scalar on the quotient spacetime AdS3/ℤ, which has the isometry group SO(2, 2) rather than its universal cover. This problem is of interest as a special example of QFT on a spacetime with closed timelike curves (CTCs), as a new context in which to study generalizations of AdS/CFT and for its role in celestial holography. A basis of time-periodic solutions to the Klein-Gordon wave equation is found in terms of hypergeometric functions. They fall into a PT even and a PT odd principal series representation, rather than the more familiar highest-weight representations of the cover of SO(2, 2). For masses below the Breitenlohner-Freedman (BF) bound, the modes fall on the unitary principal series. The presence of CTCs precludes the usual canonical quantization, but geometric quantization, which begins with a symplectic form on the phase space of classical solutions, is applicable. Operators, commutators, an SO(2, 2) invariant vacuum and a Fock space are constructed and transform like those of a CFT2. The Fock space norm is positive below the BF bound. In celestial holography, AdS3/ℤ arises as leaves of a hyperbolic foliation of Klein space. Our analysis determines new entries in the symmetry-constrained celestial bulk-to-boundary dictionary. In particular the Klein space 𝒮-matrix is dual to a maximally entangled state in the tensor product of two copies of the ‘wedge CFT2’ associated to the timelike and spacelike wedges of Klein space. Translation invariance is not present in the wedge CFT2 itself but emerges as a property of this maximally entangled state.