arXiv subjects
Publications and source records attributed to Vitaly Bornyakov.
We present new results on properties of $SU(2)$ QCD in lattice regularization. Our main goal is to find the transition line confinement - deconfinement in $μ- T$ plane. We compute the Polyakov loop and the string tension to determine this line.
We study the transverse and longitudinal gluon propagators in the Landau-gauge lattice QCD with gauge group $SU(2)$ at nonzero quark chemical potential and zero temperature. We show that both propagators demonstrate substantial dependence on the quark chemical potential. This observation contradicts to earlier findings by other groups.
A new scheme for color confinement in QCD due to violation of the non-Abelian Bianchi identities proposed earlier is revised. The violation of the non-Abelian Bianchi identities (VNABI) $J_μ$ is equal to Abelian-like monopole currents $k_μ$ defined by the violation of the Abelian-like Bianchi identities. VNABI satisfies $\partial_μJ_μ=0$. There are $N^2-1$ conserved magnetic charges in $SU(N)$ QCD. The charge of each component of VNABI is assumed to satisfy the Dirac quantization condition. %%%%% Each color component of the non-Abelian electric field $E^a$ is squeezed by the corresponding color component of the solenoidal current $J^a_μ$. Then only the color singlets alone can survive as a physical state and non-Abelian color confinement is realized. Numerical studies are done in the framework of $SU(2)$ lattice gauge theory. We adopt an Abelian-like definition of monopole following DeGrand-Toussaint as a lattice version of VNABI. To reduce severe lattice artifacts, we introduce various techniques of smoothing the thermalized vacuum such as the maximal center gauge (MCG) fixing. We measure the density $ρ(a(β),n)=\sqrt{(k_n^1)^2+(k_n^2)^2+(k_n^3)^2}/(4\sqrt{4}Vb^3)$, where $k_n^a$ is an $n$ blocked monopole in the color direction $a$ and $b=na(β)$ is the blocked lattice spacing. Beautiful scaling behaviors are seen when we plot $ρ(a(β),n)$ versus $b=na(β)$. A single universal curve $ρ(b)$ is found from $n=1\sim 12$, which suggests that $ρ(a(β),n)$ is a function of $b=na(β)$ alone. The universal curve seems independent of a gauge fixing procedure used to smooth the lattice vacuum when the scaling is obtained. The scaling shows that the lattice definition of VNABI has the continuum limit.
The disorder parameter of confinement-deconfinement phase transition based on the monopole action determined previously in $SU(2)$ QCD are investigated. We construct an operator which corresponds to the order parameter defined in the abelian Higgs model. The operator shows proper behaviors as the disorder parameter in the numerical simulations of finite temperature QCD.