论文标题
大N形成量表理论中的热顺序
Thermal order in large N conformal gauge theories
论文作者
论文摘要
在这项工作中，我们探讨了在所有非零温度下，在$ d = 4 $时空维度中自发破坏全球对称性的可能性。我们表明，这种对称性破坏确实发生在某些以平面限制的非对称性大$ n $仪表理论的家庭中。我们还表明，这种现象伴随着在任何温度下持续的BROUT-ENGLERT-HIGGS（BEH）阶段的系统。这些分析是由Arxiv：2005.03676中所做的工作激发的，在该分数中，在所有热状态下，在所有热状态下都观察到对称性破坏。 在我们的情况下，证明上述功能的理论具有一个量规组，这些量规组是一个家庭中的特定产品（n）$的特定产品，而另一个家庭则是$ su（n）$。在$ n \ rightarrow \ infty $限制下以扰动制度工作，我们表明这些理论中的beta功能在耦合空间中产生了固定点的圆圈。我们明确检查该结构最多两个循环，然后在所有循环校正下提供其生存的证明。我们表明，在某些条件下，这个固定点圆的间隔既表明了全局对称性的自发断裂以及在所有非零温度下的持续BEH阶段。损坏的全局对称性是一种理论家族中的$ \ mathbb {z} _2 $，另一个理论中的$ u（1）$。相应的顺序参数是这些理论中双歧骨标量字段的决定因素的期望值。我们将这些对称性表征为在各个模型中类似Baryon的对称性。
In this work we explore the possibility of spontaneous breaking of global symmetries at all nonzero temperatures for conformal field theories (CFTs) in $D = 4$ space-time dimensions. We show that such a symmetry-breaking indeed occurs in certain families of non-supersymmetric large $N$ gauge theories at a planar limit. We also show that this phenomenon is accompanied by the system remaining in a persistent Brout-Englert-Higgs (BEH) phase at any temperature. These analyses are motivated by the work done in arXiv:2005.03676 where symmetry-breaking was observed in all thermal states for certain CFTs in fractional dimensions. In our case, the theories demonstrating the above features have gauge groups which are specific products of $SO(N)$ in one family and $SU(N)$ in the other. Working in a perturbative regime at the $N\rightarrow\infty$ limit, we show that the beta functions in these theories yield circles of fixed points in the space of couplings. We explicitly check this structure up to two loops and then present a proof of its survival under all loop corrections. We show that under certain conditions, an interval on this circle of fixed points demonstrates both the spontaneous breaking of a global symmetry as well as a persistent BEH phase at all nonzero temperatures. The broken global symmetry is $\mathbb{Z}_2$ in one family of theories and $U(1)$ in the other. The corresponding order parameters are expectation values of the determinants of bifundamental scalar fields in these theories. We characterize these symmetries as baryon-like symmetries in the respective models.
