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Register a new user3D Yang-Mills confining properties from a non-Abelian ensemble perspective
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In this work, we propose a $3D$ ensemble measure for center-vortex worldlines and chains equipped with non-Abelian degrees of freedom. We derive an effective field description for the center-element average where the vortices get represented by $N$ flavors of effective Higgs fields transforming in the fundamental representation. This field content is required to accommodate fusion rules where $N$ vortices can be created out of the vacuum. The inclusion of the chain sector, formed by center-vortex worldlines attached to pointlike defects, leads to a discrete set of $Z(N)$ vacua. This type of SSB pattern supports the formation of a stable domain wall between quarks, thus accommodating not only a linear potential but also the Luscher term. Moreover, after a detailed analysis of the associated field equations, the asymptotic string tension turns out to scale with the quadratic Casimir of the antisymmetric quark representation. These behaviors reproduce those derived from Monte Carlo simulations in $SU(N)$ $3D$ Yang-Mills theory, which lacked understanding in the framework of confinement as due to percolating magnetic defects.
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We study the Schwinger process in a uniform non-Abelian electric field using a dynamical approach in which we evolve an initial quantum state for gluonic excitations. We evaluate the spectral energy density and number density in the excitations as functions of time. The total energy density has an ultraviolet divergence which we argue gets tamed due to asymptotic freedom, leading to $g^4E^4t^4$ growth, where $g$ is the coupling and $E$ the electric field strength. We also find an infrared divergence in the number density of excitations whose resolution requires an effect such as confinement.
We present some classical properties for non-abelian Yang-Mills theories that we extract directly from the Maxwells equations of the theory. We write the equations of motion for the SU(3) Yang-Mills theory using the language of Maxwells equations in both differential and integral forms. We show that vectorial gauge fields in this theory are non-fermionic sources for non-abelian electric and magnetic fields. These vectorial gauge fields are also responsible for the existence of magnetic monopoles. We build the continuity equation and the energy-momentum tensor for the non-abelian case.
We determine the dimension of the moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory in 2+1 dimensions for gauge groups $G=U(1)times G$ with $G$ being an arbitrary semi-simple group. The calculation is carried out using a Callias-type index theorem, the moduli matrix approach and a D-brane setup in Type IIB string theory. We prove that the index theorem gives the number of zeromodes or moduli of the non-Abelian vortices, extend the moduli matrix approach to the Yang-Mills-Chern-Simons-Higgs theory and finally derive the effective Lagrangian of Collie and Tong using string theory.
Recently, a new procedure to quantize the $SU(N)$ Yang-Mills theory in the nonperturbative regime was proposed. The idea is to divide the configuration space ${A_mu}$ into sectors labeled by different topological degrees of freedom and fix the gauge separately on each one of them. As Singers theorem on gauge copies only refers to gauge fixing conditions that are global in ${A_mu}$, this construction might avoid the Gribov problem. In this work, we present a proof of the renormalizability in the center-vortex sectors, thus establishing the calculability of the Yang-Mills center-vortex ensemble.
Various gauge invariant but non-Yang-Mills dynamical models are discussed: Precis of Chern-Simons theory in (2+1)-dimensions and reduction to (1+1)-dimensional B-F theories; gauge theories for (1+1)-dimensional gravity-matter interactions; parity and gauge invariant mass term in (2+1)-dimensions.
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