In this work, we analyze a recent proposal to detect SUðNÞ continuum Yang-Mills sectors labeled by center vortices, inspired by Laplacian-type center gauges in the lattice. Initially, after the introduction of appropriate external sources, we obtain a rich set of sector-dependent Ward identities, which can be used to control the form of the divergences. Next, we show the all-order multiplicative renormalizability of the center-vortex free sector. These are important steps towards the establishment of a first-principles, well-defined, and calculable Yang-Mills ensemble.

We study quantum effects induced by a point-like object that imposes Dirichlet boundary conditions along its world-line, on a real scalar field ϕ in 1, 2 and 3 spatial dimensions. The boundary conditions result from the strong coupling limit of a term quadratic in the field and localized on the particle's trajectory. We discuss the renormalization issues that appear and evaluate the effective action. Special attention is paid to the case of 2 spatial dimensions where the coupling constant is adimensional. arXiv:1910.12737v1 [hep-th] 28 Oct 2019 quanta when a field is subjected to time-dependent boundary conditions, an example being the presence of one or more moving mirrors, namely, of objects imposing non-trivial boundary conditions on the field. In the usual understanding of the term, a boundary condition acts on a region having co-dimension one, i.e., which is determined by a single equation. It is worth noting that, in the context of the DCE for a real scalar field, which we consider here, different kinds of boundary conditions, besides the 'perfect' ones (Dirichlet and Neumann), have also been studied. Those 'imperfect' conditions describe mirrors which have more realistic responses to the action of the field's modes. Among that kind of condition, a relatively simple one amounts to Dirichlet-like boundary conditions: they result from the addition to the action of a term localized on the space-time region which is swept by the mirror during the course of time. When the strength of that term tends to infinity, one gets Dirichlet conditions on the region on which the term is localized. It is our concern in this paper to study the DCE, for the case of a real scalar field ϕ in d + 1 dimensions (d = 1, 2, 3), coupled to point-like objects which implement precisely that kind of Dirichlet-like boundary conditions. In other words, we shall add to the scalar field Lagrangian a term proportional to a δ-function of the (time-dependent) position of the particle, and to the square of ϕ. The strength of the term is determined by a coupling constant which, by taking the appropriate limit, will be used to impose Dirichlet boundary conditions. We shall follow our previous work for scalar and spinorial vacuum fields [4,5] in which we used the particularly convenient functional approach proposed by Golestanian and Kardar [6]. The approach is based on the use of auxiliary fields to deal with the role of the mirrors, on the calculation of the functional integral for the in-out effective action. An important feature of the systems that we consider here is the following: except for d = 1 a curve, like the particle's world-line, has codimension bigger than 1; this fact results in qualitatively different UV properties during the calculation of the effective action. Indeed, the UV problems which will arise here are rather similar to the ones corresponding to Dirac δ-potentials in 2 and 3 dimensions, a system which has been extensively studied by following many different approaches and frameworks (see, for example, [7,8,9,10]). Note t...

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 Lüscher 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. * davidjunior@id.uff.br †

No abstract