Abelian Higgs model with charge conjugate boundary conditions

The Abelian Higgs model is studied on the lattice with charge conjugate boundary conditions. A locally gauge invariant operator for the charged scalar field is constructed, and the charged scalar particle mass is calculated in the Coulomb phase of the lattice model. Agreement is found with the mass calculated in Coulomb gauge. The gauge invariant scalar field operator is used to calculate the Higgs boson mass in the Higgs region and to show that the charged particle disappears from the spectrum in the confined regime.

Figure 1

Schematic phase diagram for the lattice Abelian Higgs model at fixed $\lambda$.

Figure 2

Observables calculated using the scalar field action $S_{\phi }$ with periodic boundary conditions in the absence of a gauge field.

Figure 3

Observables calculated using the scalar field action $S_{\phi }$ with charge conjugate boundary conditions in the absence of a gauge field.

Figure 4

Scalar particle mass in lattice units as a function of $\kappa$ calculated using the scalar field action in the absence of a gauge field.

Figure 5

Observables as a function of $\kappa$ calculated with the action (19) using charge conjugate boundary conditions.

Figure 6

Charged particle mass in lattice units as a function of $\kappa$ in the Coulomb phase calculated with different operators.

Figure 7

Scalar particle mass in lattice units as a function of $\kappa$ in the Higgs region calculated with different operators.

Figure 8

Observables as a function of $\beta$ calculated with the action (19) with charge conjugate boundary conditions.

Figure 9

Charged particle mass in lattice units as a function of $\beta$ calculated using the operator $\mathrm{Re}{\phi }_s$.

Figure 10

Correlation function $⟨\mathrm{Re}{\phi }_s(t)\mathrm{Re}{\phi }_s(0)⟩$ at $\beta =0.25$.

Figure 11

Ground state energy from the correlation function of the operator $O_p$ [Eq. (28)] as a function of $\beta$ calculated at momentum $(\pi /L)$ (1,1,1). The dashed line shows the energy of a zero mass particle at this momentum from the dispersion relation (26).