We study monopoles in gauge theories with generic gauge group. Magnetic charges are in one-to-one correspondence with the second homotopy classes at spatial infinity ($Π_2$), which are therefore identified by the 't Hooft tensor. We determine the 't Hooft tensor in the general case. These issues are relevant to the understanding of Color Confinement.
We discuss the lattice formulation of the 't Hooft surface, that is, the two-dimensional surface operator of a dual variable. The 't Hooft surface describes the world sheets of topological vortices. We derive the formulas to calculate the expectation value of the 't Hooft surface in the multiple-charge lattice Abelian Higgs model and in the lattice non-Abelian Higgs model. As the first demonstration of the formula, we compute the intervortex potential in the charge-2 lattice Abelian Higgs model.
As a color confinement mechanism, a dual Meissner effect due to Abelian monopoles involved in QCD has been discussed so far in various ways. But still there is an important problem unsolved. It is gauge invariance of the schemes or, in other words, the reason why non-Abelian color confinement is explained by means of the Abelian dual Meissner effect. Here it is shown that a random Abelian method based on the violation of non-Abelian Bianchi identity (VNABI) could prove SU(3) invariance and explain why color-singlets alone can survive in the confinement phase of QCD in the framework of the Abel…
The symmetries and dynamics of simple chiral $SU(N)$ gauge theories, with matter Weyl fermions in a two-index symmetric tensor and $N+4$ anti-fundamental representations, are examined, by taking advantage of the recent developments involving the ideas of generalized symmetries, gauging of discrete center 1-form symmetries and mixed 't Hooft anomalies. This class of models are particularly interesting because the conventional 't Hooft anomaly matching constraints allow a chirally symmetric confining vacuum, with no condensates breaking the $U(1) \times SU(N+4)$ flavor symmetry, and with certain…
We study the mixed anomaly between the discrete chiral symmetry and general baryon-color-flavor (BCF) backgrounds in $SU(N_c)$ gauge theories with $N_f$ flavors of Dirac fermions in representations ${\cal R}_c$ of $N$-ality $n_c$, formulated on non-spin manifolds. We show how to study these theories on $\mathbb{CP}^2$ by turning on general BCF fluxes consistent with the fermion transition functions. We consider several examples in detail and argue that matching the anomaly on non-spin manifolds places stronger constraints on the infrared physics, compared to the ones on spin manifolds (e.g.~$\…
Numerical Hints for Dyon Condensation at $θ=2π$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Department of Physics, and Research and Education Center for Natural Sciences, Keio University（庆应义塾大学物理系及自然科学研究教育中心）；RIKEN Center for Computational Science（理化学研究所计算科学中心）；Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学中心（iTHEMS））；Information Technology Center, The University of Tokyo（东京大学信息中心）；Department of Advanced Materials Science, The University of Tokyo（东京大学先进材料科学系）；Department of Information and Mathematical Sciences, Tokyo Woman’s Christian University（东京女子基督教大学信息数学科学系）；Department of Physics, Kyoto University（京都大学物理学系）
A topological $θ$-term in gauge theories, including quantum chromodynamics in 3+1 dimensions, gives rise to a sign problem that makes classical Monte Carlo simulations impractical. Quantum simulations are not subject to such sign problems and are a promising approach to studying these theories in the future. In the near term, it is interesting to study simpler models that retain some of the physical phenomena of interest and their implementation on quantum hardware. For example, dimensionally-reducing gauge theories on small spatial tori produces quantum mechanical models which, despite being …
We construct a non-trivial $U(1)/\mathbb{Z}_q$ principal bundle on~$T^4$ from the compact $U(1)$ lattice gauge field by generalizing Lüscher's constriction so that the cocycle condition contains $\mathbb{Z}_q$ elements (the 't~Hooft flux). The construction requires an admissibility condition on lattice gauge field configurations. From the transition function so constructed, we have the fractional topological charge that is $\mathbb{Z}_q$ one-form gauge invariant and odd under the lattice time reversal transformation. Assuming a rescaling of the vacuum angle $θ\to qθ$ suggested from the Witten …
We study a four-dimensional $U(1)$ gauge theory with the $θ$ angle, which was originally proposed by Cardy and Rabinovici. It is known that the model has the rich phase diagram thanks to the presence of both electrically and magnetically charged particles. We discuss the topological nature of the oblique confinement phase of the model at $θ=π$, and show how its appearance can be consistent with the anomaly constraint. We also construct the $SL(2,\mathbb{Z})$ self-dual theory out of the Cardy-Rabinovici model by gauging a part of its one-form symmetry. This self-duality has a mixed 't Hooft ano…
