New Higher Anomalies, SU(N) Yang-Mills Gauge Theory and CP^{N-1} Sigma Model

Zheyan Wang USTC Juven Wang IAS Princeton

Theoretical Physics mathscidoc:1904.39002

We hypothesize a new and more complete set of anomalies of certain quantum field theories (QFTs) and then give an eclectic proof. First, we propose a set of 't Hooft anomalies of 2d $\mathbb{CP}^{\mathrm{N}-1}$-sigma models at $\theta=\pi$, with N $=2,3,4$ and others, by enlisting all possible 3d cobordism invariants and selecting the matched terms. Second, we propose a set of 't Hooft higher anomalies of 4d time-reversal symmetric SU(N)-Yang-Mills (YM) gauge theory at $\theta=\pi$, via 5d cobordism invariants (higher symmetry-protected topological states) such that compactifying YM theory on a 2-torus matches the constrained 3d cobordism invariants from sigma models. Based on algebraic/geometric topology, QFT analysis, manifold generator dimensional reduction, condensed matter inputs and additional physics criteria, we derive a correspondence between 5d and 3d new invariants, thus broadly prove a more complete anomaly-matching between 4d YM and 2d $\mathbb{CP}^{\mathrm{N}-1}$ models via a twisted 2-torus reduction, done by taking the Poincar\'e dual of specific cohomology class with $\mathbb{Z}_2$ coefficients. We formulate a higher-symmetry analog of "Lieb-Schultz-Mattis theorem" to constrain the low-energy dynamics.
High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Lattice (hep-lat); High Energy Physics - Phenomenology (hep-ph); Algebraic Topology (math.AT)
[ Download ] [ 2019-04-28 05:46:34 uploaded by juvenwang ] [ 562 downloads ] [ 0 comments ]
  • https://arxiv.org/abs/1812.11968
@inproceedings{zheyannew,
  title={New Higher Anomalies, SU(N) Yang-Mills Gauge Theory and  CP^{N-1} Sigma Model},
  author={Zheyan Wang, and Juven Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190428054634290683285},
}
Zheyan Wang, and Juven Wang. New Higher Anomalies, SU(N) Yang-Mills Gauge Theory and CP^{N-1} Sigma Model. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190428054634290683285.
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