系综平均中的涌现对称性
Emergent Symmetries in Ensemble Averages
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- University of Tokyo（东京大学）
- Kavli Institute for Physics and Mathematics of the Universe (Kavli IPMU), UTIAS, University of Tokyo（东京大学宇宙线研究所（Kavli IPMU））
- Trans-Scale Quantum Science Institute, University of Tokyo（东京大学跨尺度量子科学研究所）
- Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））
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中文总结 AI 辅助
本文回顾并论证量子引力中全局对称性可在系综平均后涌现，以Narain型CFT为例，通过Siegel-Weil公式和Chern-Simons理论解释，并关联沼泽地计划与SWSSB，提出新猜想。
中文摘要 AI 辅助
人们普遍认为，在量子引力中不存在精确的全局对称性。我们回顾了近期研究表明，全局对称性仍可在理论的系综平均后涌现，正如在全息原理中所遇到的那样。作为一个精确的案例研究，我们讨论了与一般符号的偶二次型相关的二维Narain型共形场论的系综平均，该平均由Siegel-Weil公式计算，并被解释为三维阿贝尔Chern-Simons理论中几何求和。体态任意子的全局对称性可以在平均后涌现，因为系综中不同理论之间的T-对偶被“折叠”成单一理论的对称性（对偶折纸）。我们讨论了与沼泽地计划的关系，包括在无限距离处全局对称性的涌现。最后，我们将混合态的强到弱自发对称性破缺（SWSSB）重新解释为系综平均中对称性的涌现；在全息原理中，连接热场双重构造两侧的虫洞提供了其体态实现。这激发了一个新的沼泽地猜想。
英文摘要
It is widely believed that there are no exact global symmetries in quantum gravity. We review recent works showing that global symmetries can nevertheless emerge after ensemble averages of theories, as encountered in holography. As a precision case study, we discuss the ensemble average of two-dimensional Narain-type conformal field theories associated with an even quadratic form of general signature, which is computed by the Siegel-Weil formula and interpreted as a sum over geometries in a three-dimensional Abelian Chern-Simons theory. Global symmetries of the bulk anyons can emerge after the average, as T-dualities relating different theories in the ensemble are "folded" into symmetries of a single theory (duality origami). We discuss the relation to the Swampland program, including the emergence of global symmetries at infinite distance. Finally, we recast strong-to-weak spontaneous symmetry breaking (SWSSB) of mixed states as an emergence of symmetries in ensemble averages; in holography, wormholes connecting the two sides of a thermofield-double construction provide its bulk realization. This motivates a new Swampland conjecture.
