AI 中文总结
本研究采用大N方法解析双锥矢量模型，将2+1维等标量理论的Z₂对称性破缺构造统一，证明其可持续到任意高温，填补了相关普适类关联的空白。
AI 中文摘要
通常认为，在足够高的温度下，热涨落会破坏有序性并恢复对称性。然而，最近在2+1维中，一系列标量理论通过ε展开、FRG（重整化群流）和大N技术等多种方法被证明，其Z₂对称性破缺会持续到任意高的温度。尽管这些理论之间的相似性表明它们属于同一普适类，但这种关联尚未得到明确证实。本研究填补了这一空白：采用大N方法，在1/N展开的领头阶和次领头阶下，解析研究了双锥矢量模型在包括2+1维在内的多个时空维度的情况，确定了红外理论的RG流、不动点结构和CFT数据，重现并扩展了此前的结果，从而将看似不同的构造统一到一个共同的解析框架中；还推导了有效势，确定了其在零温及有限温度下的稳定极小值，并证明对于有限大N，Z₂对称性会在任意高温度下发生自发破缺。
英文摘要
Thermal fluctuations are generally expected to destroy order and restore symmetries at sufficiently high temperatures. Recently, however, a family of scalar theories in $2+1$ dimensions was shown to exhibit $\mathbb Z_2$ symmetry breaking that persists to arbitrarily high temperatures using a variety of approaches, including the $ε$-expansion, the FRG, and large-$N$ techniques. Although the similarities among these theories suggest that they belong to the same universality class, this connection has not been established explicitly. In this work, we fill this gap. Using large-$N$ methods, we analytically study the biconical vector model in a range of spacetime dimensions, including $2+1$, at leading and next-to-leading order in the $1/N$ expansion. We determine the RG flow, fixed-point structure, and the CFT data of the infrared theory, reproducing and extending previous results and thereby unifying the apparently distinct constructions within a common analytic framework. We derive the effective potential, establish its stable minima at zero and finite temperature, and demonstrate spontaneous $\mathbb{Z}_2$ symmetry breaking at arbitrarily high temperatures for large finite $N$.
Comments30+10 pages, 1 figure, 1 table
