引导弱破缺规范理论在（反）德西特空间中的自举方法

中文摘要 AI 辅助

我们发展了一种用于（反）德西特空间中弱破缺规范理论的自举方法，重点关注对偶边界流守恒被双迹算符破坏的情形。通过积分相应的Ward恒等式，我们推导出赝荷守恒恒等式，其中包含作为三点函数积分的固定非局域贡献。这些恒等式对允许的理论空间施加了一致性条件。作为示例，我们研究了AdS中具有对称性破缺边界条件的带电物质杨-米尔斯理论，并表明赝荷守恒恒等式约束了两个量子化扇区之间的混合。随后，我们将该框架应用于具有共同边界的两个AdS空间中引力的Higgs机制，这两个空间耦合使得相应的应力张量不分别守恒。在这种设置下，普通荷守恒恒等式恢复了分解为两个独立CFT的结果，而赝荷守恒恒等式对对称性破缺参数的任意值均成立。最后，对于德西特空间中的共形引力，我们约束了引力子与部分无质量自旋-2场之间的相互作用，既在最小理论中，也在存在额外标量或矢量物质的情况下，发现与相应体理论预测一致。

英文摘要

We develop a bootstrap approach for weakly broken gauge theories in (anti-)de Sitter space, focusing on cases in which the conservation of the dual boundary current is broken by a double-trace operator. Integrating the corresponding Ward identity, we derive pseudo-charge conservation identities that contain fixed nonlocal contributions as integrals of three-point functions. These identities impose consistency conditions on the space of allowed theories. As an illustrative example, we study Yang-Mills theory in AdS with symmetry-breaking boundary conditions for charged matter and show that the pseudo-charge conservation identities constrain the mixing between the two quantization sectors. We then apply the framework to the Higgs mechanism for gravity in two AdS spaces with a common boundary, coupled so that the corresponding stress tensors are not separately conserved. In this setting, the ordinary charge conservation identities recover the factorization into two independent CFTs, whereas the pseudo-charge conservation identities hold for arbitrary values of the symmetry-breaking parameter. Finally, for conformal gravity in de Sitter space, we constrain the interactions between the graviton and the partially massless spin-2 field, both in the minimal theory and in the presence of additional scalar or vector matter, finding agreement with the predictions of the corresponding bulk theories.

发表机构

• University of Cambridge（剑桥大学）
• Leung Center for Cosmology and Particle Astrophysics（梁林宇宙学与粒子天体物理中心）
• Case Western Reserve University（凯斯西储大学）
• University of Arizona（亚利桑那大学）
• University of Amsterdam（阿姆斯特丹大学）

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64 pages, 1 figure