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Register a new userRenormalizability of a first principles Yang-Mills center-vortex ensemble
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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.
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In this work, we analyzed a recent proposal to detect $SU(N)$ 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 obtained a rich set of sector-dependent Ward identities, which can be used to control the form of the divergences. Next, we were able to 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.
Maximal t Hooft loops are studied in SO(3) lattice gauge theory at finite temperature T. Tunneling barriers among twist sectors causing loss of ergodicity for local update algorithms are overcome through parallel tempering, enabling us to measure the vortex free energy F and to identify a deconfinement transition at some $beta_A^{crit}$. The behavior of F below $beta_A^{crit}$ shows however striking differences with what is expected from discretizations in the fundamental representation.
The center vortex model for the infrared sector of SU(3) Yang-Mills theory is reviewed. After discussing the physical foundations underlying the model, some technical aspects of its realisation are discussed. The confining properties of the model are presented in some detail and compared to known results from full lattice Yang-Mills theory. Particular emphasis is put on the new phenomenon of vortex branching, which is instrumental in establishing first order behaviour of the SU(3) phase transition. Finally, the vortex free energy is verified to furnish an order parameter for the deconfinement phase transition. It is shown to exhibit a weak discontinuity at the critical temperature, in agreement with predictions from lattice gauge theory.
We show that pure Yang-Mills theories with Lorentz violation are renormalizable to all orders in perturbation theory. To do this, we employ the algebraic renormalization technique. Specifically, we control the breaking terms with a suitable set of external sources which, eventually, attain certain physical values. The Abelian case is also analyzed as a starting point. The main result is that the renormalizability of the usual Maxwell and Yang-Mills sectores are both left unchanged. Furthermore, in contrast to Lorentz violating QED, the odd CPT violation sector of Yang-Mills theories renormalizes independently. Moreover, the method induces, in a natural way, mass terms for the gauge field while the photon remains massless (at least n the sense of a Proca-like term). The entire analysis is carried out at the Landau gauge.
Recently, based on a new procedure to quantize the theory in the continuum, it was argued that Singers theorem points towards the existence of a Yang-Mills ensemble. In the new approach, the gauge fields are mapped into an auxiliary field space used to separately fix the gauge on different sectors labeled by center vortices. In this work, we study this procedure in more detail. We provide examples of configurations belonging to sectors labeled by center vortices and discuss the existence of nonabelian degrees of freedom. Then, we discuss the importance of the mapping injectivity, and show that this property holds infinitesimally for typical configurations of the vortex-free sector and for the simplest example in the one-vortex sector. Finally, we show that these configurations are free from Gribov copies.
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