Abstract SU(3) gauge theory in the nonlinear gauge of the Curci–Ferrari type is studied. In the low-energy region, ghost condensation and subsequent gauge field condensation can happen. The latter condensation makes classical gauge fields massive. If the color electric potential with a string is chosen as the classical gauge field, it produces the static potential with the linear potential. We apply this static potential to the three-quark system, and show, differently from the Y-type potential, that infrared divergence remains in the Δ-type potential. The color electric flux is also studied, showing that a current which plays the role of the magnetic current appears

Japan

Hirohumi Sawayanagi

Condensates, massive gauge fields, and confinement in the SU(3) gauge theory

Abstract  potential is studied in the SU(2) gauge theory. Based on the nonlinear gauge of the Curci–Ferrari type, the possibility of a gluon condensation  in a low-energy region has been considered at the one-loop level. Instead of the magnetic monopole condensation, this condensation makes classical gluons massive, and can yield a linear potential. We show that this potential consists of the Coulomb plus linear part and an additional part. Comparing with the Cornell potential, we study this confining potential in detail, and find that the potential has two implicit scales:  and . The meanings of these scales are clarified. We also show that the Cornell potential that fits well to this confining potential is obtained by taking these scales into account.

Confining potential under the gauge field condensation in the SU(2) Yang–Mills theory

Abstract SU(2) gauge theory in the nonlinear gauge of Curci–Ferrari type is studied in the low-energy region. We give a classical solution that connects color electric charges. Its dual solution, which has a monopole configuration, is also presented. Due to gluon condensation subsequent to the ghost condensation, these classical fields become massive. The massive Lagrangian with the classical solution and that with the dual solution are derived. We show that these Lagrangians produce a linear potential between a quark and an antiquark. This is the mechanism of quark confinement, which is different from magnetic monopole condensation.

Massive dual gauge field and confinement in Minkowski space: Electric charge

Abstract Gauge field configuration for a magnetic monopole and its dual configuration are studied in SU(2) gauge theory. We present a relation between the monopole field and its dual field. Since these fields can become massive, their massive Lagrangians are derived. In the dual case, an additional term appears. We show that this term is necessary to produce a linear potential between a monopole charge and an antimonopole charge.

Massive dual gauge field and confinement in Minkowski space: Magnetic charge

Euclidean SU(2) gauge theory is studied in a nonlinear gauge. In this theory, ghost condensation happens and gauge fields acquire tachyonic masses. It is shown that these tachyonic masses are removed by a gauge field condensate . Because of the ghost condensation, monopole solutions are included naturally. We find that the condensate makes the magnetic potential massive.

Condensate and massive magnetic potential in Euclidean gauge theories

The effect of the Gribov horizon in Euclidean SU(2) gauge theory is studied. Gauge fields on the Gribov horizon yield zero modes of ghosts and antighosts. We show these zero modes can produce additional ghost interactions, and the Landau gauge changes to a nonlinear gauge effectively. In the infrared limit, however, the Landau gauge is recovered, and ghost zero modes may appear again. We show ghost condensation happens in the nonlinear gauge, and the zero mode repetition is avoided.