论文标题
类似矢量和手性颤抖的理论之间的通用性：异常和域墙
Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls
论文作者
论文摘要
我们研究了$ [su（n）]^k $手性颤动仪的低能动力学，与$ \ Mathcal {n} = 1 $ super yang-mills（sym）理论以及带有双重界面费（qcd（bf））的量子彩色动力学。这些理论可以通过$ \ mathbb {z} _k $ orbifold的$ \ mathcal {n} = 1 $ $ $ su（nk）$ sym理论的投影，但是扰动的平面等价并不是$ k \ e ge 3 $的非扰动性扩展。为了研究低能行为，我们使用$ \ mathbb {r}^3 \ times s^1 $上的“ t〜hooft异常匹配且可靠的半典型”分析了这些系统。多亏了涉及$ 1 $的中心对称性和离散手性对称性的't〜hooft异常，我们预测手性对称性必须在禁闭阶段自发折断，并且存在$ n $ vacua。尽管存在无质量费米，但具有$ k $的理论具有物理$θ$角，我们进一步预测了与之相关的$ n $分支结构；由于自发$ cp $ breaking，$θ=π$在$θ=π$上的真空数量增加到$ 2N $。这两个预测均通过可靠的半典型学明确确认，并在$ \ mathbb {r}^3 \ times s^1 $带有双跟踪变形。奇数 - $ k $理论的对称和异常与$ {\ cal n} = 1 $ sym的对称性和异常相同，而均匀的$ k $理论的理论与qCD（bf）的理论相同。我们揭示了为什么类似矢量和手性颤动理论之间存在普遍性，并猜想他们的基态可以在没有量子相变的情况下连续变形。我们简要讨论连接该理论真空的域壁上的异常流入以及可能的异常匹配场景。
We study low-energy dynamics of $[SU(N)]^K$ chiral quiver gauge theories in connection with $\mathcal{N}=1$ super Yang-Mills (SYM) theory, and quantum chromodynamics with bi-fundamental fermions (QCD(BF)). These theories can be obtained by $\mathbb{Z}_K$ orbifold projections of $\mathcal{N}=1$ $SU(NK)$ SYM theory, but the perturbative planar equivalence does not extend nonperturbatively for $K\ge 3$. In order to study low-energy behaviors, we analyze these systems using 't~Hooft anomaly matching and reliable semiclassics on $\mathbb{R}^3\times S^1$. Thanks to 't~Hooft anomaly that involves $1$-form center symmetry and discrete chiral symmetry, we predict that chiral symmetry must be spontaneously broken in the confinement phase, and there exist $N$ vacua. Theories with even $K$ possess a physical $θ$ angle despite the presence of massless fermions, and we further predict the $N$-branch structure associated with it; the number of vacua is enhanced to $2N$ at $θ=π$ due to spontaneous $CP$ breaking. Both of these predictions are explicitly confirmed by reliable semiclassics on $\mathbb{R}^3\times S^1$ with the double-trace deformation. Symmetry and anomaly of odd-$K$ theories are the same as those of the ${\cal N}=1$ SYM, and the ones of even-$K$ theories are same as those of QCD(BF). We unveil why there exists universality between vector-like and chiral quiver theories, and conjecture that their ground states can be continuously deformed without quantum phase transitions. We briefly discuss anomaly inflow on the domain walls connecting the vacua of the theory and possible anomaly matching scenarios.
