Quantum 4d Yang-Mills theory and time-reversal symmetric 5d higher-gauge topological field theory
Quantum 4d Yang-Mills theory and time-reversal symmetric 5d higher-gauge topological field theory
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量子 4d Yang-Mills 理论和时间反转对称 5d 高规范拓扑场论
DOI：
10.1103/physrevd.100.085012
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发表时间：
2019-04
影响因子：
5
通讯作者：
Zheng Yunqin
中科院分区：
文献类型：
--
作者：
Wan Zheyan;Wang Juven;Zheng Yunqin
我们探索了作为5D有隙短/长程纠缠(SRE/LRE)拓扑态边界条件的各种4DYang-Mills规范理论(YM)。具体地说，我们通过打开时间反转(即在不可定向流形上)和一形式中心整体对称性的背景场，探索了在θ=π[SU(2)θ=πym]上具有第二类拓扑项的SU(2)规范群的4D时间反转对称纯Ym。我们发现了SU(2)θ=πym的四个兄弟姐妹，它们与背景场有不同的耦合，标记为(K1，K2)：K1=0，1表示Kramers单线/双线威尔逊线和新的混合高阶Hooft反常；K2=0，1表示玻色子/费米子威尔逊线和一个新的类似Wess-Zumino-Witten的反项。高阶反常表明，为了在n个单形上局部实现所有的高阶n-整体对称性，4d理论成为5d高阶对称性保护的拓扑态的边界(SPTS，作为数学中的可逆拓扑量子场论(ITQFT)或协边不变量，或作为凝聚态中的5d高阶对称相互作用的拓扑超导体)。通过Weyl规范原理，通过动态测量一种形式的对称性，我们将5d的体相干态变换为LRE对称性丰富的拓扑有序态(SETS)，从而得到了具有动态高形规范场的4DSO(3)θ=πym-5dLRE-高阶集合耦合系统。我们进一步导出了扩展对象的新的奇异任意子统计，例如两个世界弦和三个世界体积的膜，物理特征为5d集。我们发现了潜在地与基本的5d高规范拓扑量子场理论相关的三重和四重链接不变量，暗示了非超对称4d纯ym和5d拓扑链之间的一种新的内在联系。我们给出了4d-5d晶格单纯复正则，并桥接到4d SU(2)-和SO(3)规范量子自旋液体作为(3+1)维的实现。
We explore various 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short-/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at θ=π [SU(2)θ=π YM], by turning on the background fields for both the time reversal (i.e., on unorientable manifolds) and the one-form center global symmetry. We find four siblings of SU(2)θ=π YM with distinct couplings to background fields, labeled by (K1,K2): K1=0, 1 specifies Kramers singlet/doublet Wilson line and new mixed higher ’t Hooft anomalies; K2=0, 1 specifies the boson/fermionic Wilson line and a new Wess-Zumino-Witten–like counterterm. Higher anomalies indicate that to realize all higher n-global symmetries locally on n simplices, the 4d theory becomes a boundary of a 5d higher-symmetry-protected topological state (SPTs, as an invertible topological quantum field theory (iTQFT) or a cobordism invariant in math, or as a 5d higher-symmetric interacting topological superconductor in condensed matter). Via Weyl’s gauge principle, by dynamically gauging the one-form symmetry, we transform 5d bulk SRE SPTs into an LRE symmetry-enriched topologically ordered state (SETs); thus we obtain the 4d SO(3)θ=π YM-5d LRE-higher-SETs coupled system with dynamical higher-form gauge fields. We further derive new exotic anyonic statistics of extended objects such as two world sheets of strings and three world volumes of branes, physically characterizing the 5d SETs. We discover triple and quadruple link invariants potentially associated with the underlying 5d higher-gauge topological quantum field theories, hinting at a new intrinsic relation between nonsupersymmetric 4d pure YM and topological links in 5d. We provide 4d-5d lattice simplicial complex regularizations and bridge to 4d SU(2)- and SO(3)-gauged quantum spin liquids as (3+1)-dimensional realizations.
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影响因子：
8.6
作者：
A. Chan;P. Ye;S. Ryu
通讯作者：
A. Chan;P. Ye;S. Ryu
影响因子：
3.7
作者：
Søren Galatius;I. Madsen;U. Tillmann;M. Weiss
通讯作者：
Søren Galatius;I. Madsen;U. Tillmann;M. Weiss
影响因子：
4.4
作者：
J. Wess;B. Zumino
通讯作者：
J. Wess;B. Zumino
影响因子：
5.4
作者：
Po-Shen Hsin;Alex Turzillo
通讯作者：
Po-Shen Hsin;Alex Turzillo
DOI：
10.1063/1.2820084
发表时间：
1985
期刊：
--
影响因子：
--
作者：
S. Coleman;S. Treiman
通讯作者：
S. Coleman;S. Treiman