Monopoles of the Dirac type and color confinement in QCD

Tsuneo Suzuki,Atsuki Hiraguchi,Katsuya Ishiguro

doi:10.1051/epjconf/202225802005

Tsuneo Suzuki, Atsuki Hiraguchi + Show 1 more

Open Access

https://doi.org/10.1051/epjconf/202225802005

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Abstract

We present results of SU(3) Monte-Carlo studies of a new color confinement scheme proposed recently due to Abelian-like monopoles of the Dirac type corresponding in the continuum limit to violation of the non-Abelian Bianchi identities (VNABI). The simulations are done without any additional gauge-fixing smoothing the vacuum. We get for the first time, in pure SU(3) simulations, (1) the perfect Abelian dominance with respect to the static potentials on (12 ~ 16)4 at β = 5.6 − 5.8 using the multilevel method, (2) the monopole as well as Abelian dominances with respect to the static potentials by evaluating the Polyakov-loop correlators on 243 × 4 at β = 5.6. The Abelian photon part gives zero string tension. The new SU(3) as well as the previous SU(2) results are consistent with the new Abelian picture of color confinement that each one of eight colored electric flux is squeezed by the corresponding colored Abelian-like monopole of the Dirac type corresponding to VNABI.

Highlights

Color confinement in quantum chromodynamics (QCD) is still an important unsolved problem
As a picture of color confinement, ’t Hooft [1] and Mandelstam [2] conjectured that the QCD vacuum is a kind of a magnetic superconducting state caused by condensation of magnetic monopoles and an effect dual to the Meissner effect works to confine color charges
Color magnetic monopoles appear as a topological object at the space-like points corresponding to the singulariry of the gauge-fixing matrix

Summary

Introduction

Color confinement in quantum chromodynamics (QCD) is still an important unsolved problem. As a picture of color confinement, ’t Hooft [1] and Mandelstam [2] conjectured that the QCD vacuum is a kind of a magnetic superconducting state caused by condensation of magnetic monopoles and an effect dual to the Meissner effect works to confine color charges This conjecture is very interesting, but there are many problems to be unsolved even at the present stage. 2) Especially, consider a Polyakov gauge in which Polyakov loops are diagonalized In this gauge, the Abelian dual Meissner picture works good [13], where space-like monopole currents play the role of the solenoidal current squeezing the electric field. The Abelian dual Meissner picture works good [13], where space-like monopole currents play the role of the solenoidal current squeezing the electric field This fact is in contradiction with the ’tHooft idea[10]. In this report, (1) the new theoretical scheme for color confinement based on the dual Meissner effect due to the above monopoles is summarized shortly. (2) The first results showing the perfect Abelian dominance and the monopole dominance in pure S U(3 lattice QCD are shown along with the short review of pure S U(2) results[11]. (3) numerical results showing the continuum limit of the new monopoles[16, 17] are reviewed shortly in the framework of pure S U(2) lattice QCD, since existence of the continuum limit is essentially important for the new confinement scheme

Equivalence of VNABI and Abelian-like monopoles

The continuum limit of the new Abelian-like monopoles