Modified instanton sum in QCD and higher-groups

DOI10.1007/JHEP03(2020)123zbMATH Open1435.83187arXiv1912.01033OpenAlexW2994467208MaRDI QIDQ2191718

Author name not available (Why is that?)

Publication date: 25 June 2020

Published in: (Search for Journal in Brave)

Abstract: We consider the $SU(N)$ Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of $p$. We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both $2pi$-periodic scalar and $3$-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only $mathbb{Z}_N$ $1$-form symmetry but also $mathbb{Z}_p$ $3$-form symmetry, and we study the global nature of this theory from the recent 't Hooft anomaly matching. The computation of 't Hooft anomaly incorporates an intriguing higher-group structure. We also carefully examine that how such kinematical constraint is realized in the dynamics by using the large-$N$ and also the reliable semiclassics on $mathbb{R}^{3}imes{S}^1$, and we find that the topological susceptibility plays a role of the order parameter for the $mathbb{Z}_p$ $3$-form symmetry. Introducing a fermion in the fundamental or adjoint representation, we find that the chiral symmetry becomes larger than the usual case by $mathbb{Z}_p$, and it leads to the extra $p$ vacua by discrete chiral symmetry breaking. No dynamical domain wall can interpolate those extra vacua since such objects must be charged under the $3$-form symmetry in order to match the 't Hooft anomaly.

Full work available at URL: https://arxiv.org/abs/1912.01033

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Modified instanton sum in QCD and higher-groups

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2191718)