Correlation between Instantons and QCD-monopoles in the Abelian Gauge
Abstract
The correlation between instantons and QCD-monopoles is studied both in the lattice gauge theory and in the continuum theory. From a simple topological consideration, instantons are expected to live only around the QCD-monopole trajectory in the abelian gauge. First, the instanton solution is analytically studied in the Polyakov-like gauge, where
A
4
(x)
is diagonalized. The world line of the QCD-monopole is found to be penetrate the center of each instanton inevitably. For the single-instanton solution, the QCD-monopole trajectory becomes a simple straight line. On the other hand, in the multi-instanton system, the QCD-monopole trajectory often has complicated topology including a loop or a folded structure, and is unstable against a small fluctuation of the location and the size of instantons. We also study the thermal instanton system in the Polyakov-like gauge. At the high-temperature limit, the monopole trajectory becomes straight lines in the temporal direction. The topology of the QCD-monopole trajectory is drastically changed at a high temperature. Second, the correlation between instantons and QCD-monopoles is studied in the maximally abelian (MA) gauge and/or the Polyakov gauge using the SU(2) lattice with
16
4
. The abelian link variable
u
μ
(s)
is decomposed into the singular (monopole-dominating) part
u
Ds
μ
(s)
and the regular (photon-dominating) part
u
Ph
μ
(s)
. The instanton numbers,
Q(Ds)
and
Q(Ph)
, are measured using the SU(2) variables,
U
Ds
μ
(s)
and
U
Ph
μ
(s)
, which are reconstructed by multiplying the off-diagonal matter factor to
u
Ds
μ
(s)
and
u
Ph
μ
(s)
, respectively. A strong correlation is found between
Q(Ds)
in the singular part and the ordinary topological charge
Q(SU(2))
even after the Cabibbo-Marinari