Scholarlink

<p>We describe how to construct an effective Hamiltonian for leading twist states in <i>d</i> ≥ 3 CFTs based on the separation of scales that emerges at large spin <i>J</i> between the AdS radius <i>ℓ</i><sub>AdS</sub> and the characteristic distance ~<i>ℓ</i><sub>AdS</sub> log <i>J</i> between particles rotating in AdS with angular momentum <i>J</i>. As a controlled example, we work specifically with the toy model of a bulk complex scalar field <i>ϕ</i> with a <i>λ</i>|<i>ϕ</i>|<sup>4</sup> coupling in AdS, up to <i>O</i>(<i>λ</i><sup>2</sup>). For a given choice of twist cutoff Λ<sub><i>τ</i></sub> in the effective theory, interactions are separated into long-distance nonlocal potential terms, arising from <i>t</i>-channel exchange of states with twist ≤ Λ<sub><i>τ</i></sub>, and short-distance local terms fixed by matching to low spin CFT data. At <i>O</i>(<i>λ</i><sup>2</sup>), the effective Hamiltonian for the toy model has two-body nonlocal potential terms from one-loop bulk diagrams as well as three-body nonlocal potential terms from tree-level exchange of <i>ϕ</i>. We describe in detail how these contributions are evaluated and how they are related to the CFT data entering in the large spin expansion. We discuss how to apply the construction of such effective Hamiltonians for models which do not have a large central charge or a sparse spectrum and are not typically considered holographic.</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

Towards large-spin effective theory. Part I. Three-particle states in AdS ϕ4 theory

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月1日

查看全文
  • Giulia Fardelli,
  • A. Liam Fitzpatrick,
  • Wei Li

摘要

We describe how to construct an effective Hamiltonian for leading twist states in d ≥ 3 CFTs based on the separation of scales that emerges at large spin J between the AdS radius ℓAdS and the characteristic distance ~ℓAdS log J between particles rotating in AdS with angular momentum J. As a controlled example, we work specifically with the toy model of a bulk complex scalar field ϕ with a λ|ϕ|4 coupling in AdS, up to O(λ2). For a given choice of twist cutoff Λτ in the effective theory, interactions are separated into long-distance nonlocal potential terms, arising from t-channel exchange of states with twist ≤ Λτ, and short-distance local terms fixed by matching to low spin CFT data. At O(λ2), the effective Hamiltonian for the toy model has two-body nonlocal potential terms from one-loop bulk diagrams as well as three-body nonlocal potential terms from tree-level exchange of ϕ. We describe in detail how these contributions are evaluated and how they are related to the CFT data entering in the large spin expansion. We discuss how to apply the construction of such effective Hamiltonians for models which do not have a large central charge or a sparse spectrum and are not typically considered holographic.