Related papers: Further discussion of Tomboulis' approach to the c…
We solve Schr\"odinger's equation for the ground-state of {\it four}-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading order approximation are reduced to a…
We have previously found analytically a very unusual and unexpected form of confinement in SU(3) Yang-Mills theory. This confinement occurs in the deconfined phase of the theory. The free energy of a single static test quark diverges, even…
A model for the quantum effective description of the vacuum structure of thermalized SU(3) Yang-Mills theory is proposed. The model is based on Abelian projection leading to a Ginzburg-Landau theory for the magnetic sector. The possibility…
In order to clarify the mechanism of quark confinement in the Yang-Mills theory with mass gap, we propose to investigate the massive Yang-Mills model, namely, Yang-Mills theory with ``a gauge-invariant gluon mass term'', which is to be…
We summarize and extend evidence that the deconfinement phase transition in Yang-Mills theories can be viewed as change of effective non-perturbative degrees of freedom and of symmetries of their interactions. In short, the strings in four…
The relationship between the nonperturbative Green's functions of Yang-Mills theory and the confinement potential is investigated. By rewriting the generating functional of quantum chromodynamics in terms of a heavy quark mass expansion in…
We prove that in the limit of the coupling going to infinity a Yang-Mills theory is equivalent to a $\lambda\phi^4$ theory with the dynamics ruled just by a homogeneous equation. This gives explicitly the Green function and the mass…
By considering specific limits in the gauge coupling constant of pure Yang--Mills dynamics, it is shown how there exist topological quantum field theory sectors in such systems defining nonperturbative topological configurations of the…
We construct simple qubit-regularized Hamiltonian lattice gauge theories formulated in the monomer--dimer--tensor-network (MDTN) basis that are free of sign problems in the pure gauge sector. These models naturally realize both confined and…
We consider the partially-deconfined saddle of large-$N$ pure Yang-Mills theory lying between confined and deconfined phases, in which the color degrees of freedom split into confined and deconfined sectors. Based on the microscopic…
Strong coupling dynamics of Yang--Mills theories with chiral fermion content remained largely elusive despite much effort over the years. In this work, we propose a dynamical framework in which we can address non-perturbative properties of…
Effective Polyakov loop theories are a useful tool for an investigation of pure Yang-Mills theory and full QCD. A systematic derivation of the effective action can be done in a spatial strong coupling expansion. Quite accurate predictions…
This work is a step towards merging the ideas that arise from semi-classical methods in continuum QFT with analytic/numerical lattice field theory. In this context, we consider Yang-Mills theories coupled to fermions in the adjoint…
Quantized Yang-Mills fields lie at the heart of our understanding of the strong nuclear force. To understand the theory at low energies, we must work in the strong coupling regime. The primary technique for this is the lattice. While…
The confinement of quarks is one of the enduring mysteries of modern physics. There is a longstanding physics heuristic that confinement is a consequence of `unbroken center symmetry'. This article gives mathematical confirmation of this…
The vortex picture of confinement is studied. The deconfinement phase transition is explained as a transition from a phase in which vortices percolate to a phase of small vortices. Lattice results are presented in support of this scenario.…
We introduce a novel observable associated to Abelian monopole currents defined in the Maximal Abelian Projection of SU(3) Yang-Mills theory that captures the topology of the current loop. This observable, referred to as the…
We continue our investigation of quark confinement using a particular variant of the Cho-Duan-Ge gauge independent Abelian decomposition. The decomposition splits the gauge field into a restricted Abelian part and a coloured part in a way…
The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is the first step towards this goal. This…
Computing the entanglement entropy in confining gauge theories is often accompanied by puzzles and ambiguities. In this work we show that compactifying the theory on a small circle $\mathbb S^1_L$ evades these difficulties. In particular,…