arXiv:1812.11968 [pdf, ps, other]

**New Higher Anomalies, SU(N) Yang-Mills Gauge Theory and ℂℙN−1 Sigma Model**

Zheyan Wan, Juven Wang

Subjects: High Energy Physics – Theory (hep-th)

We hypothesize a new and more complete set of anomalies of quantum field theories (QFTs) and then give an eclectic proof. First, we propose a set of 4d ‘t Hooft higher anomalies of time-reversal symmetric SU(N)-Yang-Mills (YM) gauge theory at θ=π, specifically at N=2,3,4 and others, by enlisting all possible 5d cobordism invariants (higher symmetry-protected topological states) and selecting the matched terms. Second, we propose a set of 3d ‘t Hooft anomalies of ℂℙN−1-sigma model obtained via compactifying YM theory on a 2-torus, and select the matched 3d cobordism invariants. Based on algebraic/geometric topology, QFT analysis, manifold generator dimensional reduction, condensed matter inputs and additional physical criteria, we derive a correspondence between 5d and 3d new invariants, thus broadly prove a more complete anomaly-matching between 4d YM and 2d ℂℙN−1 models via a 2-torus reduction. We formulate a higher-symmetry analog of “Lieb-Schultz-Mattis theorem” to constrain the low-energy dynamics. Continue reading New Publications by Juven Wang