Dual QCD, confinement potential and thermal effects

Abstract

Based on the topological structure of non-Abelian gauge theories, a dual QCD gauge formulation has been developed in terms of magnetic symmetry, which manifests the topological structure of the symmetry group in a non-trivial way. The dynamical configuration of the resulting dual QCD vacuum and its flux tube configuration have been investigated for analyzing the nonperturbative features of QCD. Utilizing the dual QCD Lagrangian in the dynamically broken phase of magnetic symmetry and applying Zwanziger formalism, the non-perturbative gluon propagator has been derived and used to extract the quark confining potential for both quenched and full QCD. The quenched confining mechanism is responsible for linear confinement and points towards the permanent confinement of the colored quarks inside the hadrons. In full QCD due to lightquark polarization the quark-antiquark potential automatically screens signaling the instability in the flux tube at large inter-quark distances and such screening increases with the increase of infrared cutoff. Using the partition function approach alongwith the mean-field treatment for the QCD monopole field the thermal response of the QCD vacuum has been analyzed by deriving the finite-temperature form of quark confining potential. A continuous vanishing of the associated string tension has been observed in the vicinity of critical temperature, which, in turn, leads to the restoration of magnetic symmetry in the domain of high temperatures and signals the onset of second-order deconfinement phase transition.

Monopole Condensation and Dynamical Chiral Symmetry Breaking in Dual QCD Formulation

“…The theoretical description of QCD [16][17][18][19][20][21][22][23][24][25] within a symmetry preserving framework has been discussed. The homotomy 2 (G/H ) → 2 (SU (3)/U (1) ⊗ U (1)) produces the topological charges, obtaining the following form,…”

A non-perturbative approach to the study of confinement-deconfinement phase transition in S U(3) dual QCD formulation

“…The S U(3) dual QCD formulation is distinct from the typical QCD, i.e. the gauge potential may be expressed in terms of the local as well as topological degrees of freedom [20][21][22][23][24][25][26][27]. The local degrees of freedom remains unrestricted, while the topological degrees of freedom may be characterized by two internal killing vectors, m and m respectively.…”

Confinement, Chiral Symmetry Breaking and it's Restoration using Dual QCD Formalism

“…For the case of the simplest non-abelian gauge group, G = S U(2) [6][7][8][9][10][11][12] with its little group H as U(1), the multipletm may thus be viewed to identify the homotopy of the mapping π 2 (S 2 ) in the following form,m :…”