Topology, symmetry, and phase transitions in lattice gauge ... - tuprints

104 fractional electric charge and quark confinement
2
1.6
π, SU(2)
ρ, SU(2)
π, SU(2)×U(1)
ρ, SU(2)×U(1)
am
1.2
0.8
0.4
0.16 0.18 0.2 0.22 0.24
κ
(a) Meson masses in lattice units on a 16 × 8 3 lattice in the Coulomb
phase, βem = 2, with β col = 1.7. The chosen values of β col and
κ allow for a crosscheck with Ref. [158]. ‘SU(2)’ results are from
standard 2-color QCD. Masses in the ‘SU(2)×U(1)’ model exhibit a
radical shift of scale. Much larger values of κ are required in order
to obtain an equivalent ratio of ρ and π masses at a given β col .
2
1.6
am
1.2
0.8
0.4
κ = 0.178
(b) Meson masses in lattice units on a 16 × 8 3 lattice at β em = 2, with β col = 1.7,
as in Fig. 5.7a above, here for fixed κ = 0.178. ‘SU(2)’ results are from standard
2-color QCD with dynamical quarks, and ‘quenched’ with static quarks.
The additional jump to the ‘SU(2)×U(1)’ results indicate the topological contribution
of a Z 2 ⊂ U(1) string to the confining potential.
5.3.3.1 Correlation of SU(2) and U(1) sectors
One might wonder if dynamical quarks have effectively been removed from the
functional integral via their U(1) coupling, as far as the SU(2) sector is concerned.
This would be true if the Z 2 ⊂ U(1) phases were in fact random. Then for each SU(2)
gauge configuration, every quark loop would cancel against another that differs
only by a phase factor −1 ∈U(1) when the integration over U(1) configurations is
performed.
Remember, however, that quarks loops induce a coupling that favors a correlation
between SU(2) and U(1) links. This back-reaction is evident in the hopping expansion
effective action Eq. (5.34), which is minimized when the product of SU(2) and
U(1) degrees of freedom is unity.