$U(1)$ gauge field localization on a Bloch brane with Chumbes-Holf da Silva-Hott mechanism

We follow the Chumbes–Holf da Silva–Hott mechanism to study the (quasi)localization of the $U(1)$ gauge field on the Bloch brane. The localization and resonances of the $U(1)$ gauge field are discussed for four kinds of Bloch brane solutions: the original and generalized Bloch brane solutions, as well as the degenerate Bloch brane solutions I and II. With the Chumbes–Holf da Silva–Hott mechanism, we find that the mass spectrum of the gauge field Kaluza-Klein modes is continuous and there is no tachyonic mode. The zero mode is localized on all the branes and there are resonant Kaluza-Klein modes on the degenerate Bloch branes.

Figure 1

The shapes of the effective potential $V(z)$ and ${\tilde{\rho }}_n(z)$ for the original Bloch brane solution. The parameters are set to for $b=0.4$, $m^2=0.2$ (left), and $m^2=1$ (right).

Figure 2

The shapes of the effective potential $V(z)$ for the original Bloch brane solution with different values of the parameter $b$.

Figure 3

The shapes of $P(m)$ as a function of $m$ for different values of the parameter $b$ for the original Bloch brane solution.

Figure 4

The shapes of the effective potential $V(z)$ with different values of the parameter $c_0$ for the degenerate Bloch brane solutions I (16) (left) and II (17) (right). The other parameters are set to $v=1$ and $b=1$.

Figure 5

The $P-m$ curves for the degenerate Bloch brane solution I (16). The parameters are set to $b=1$, $v=1$, $c_0=-2-10^{-10}$ ($d=10$) (Left), and $c_0=-2-10^{-20}$ ($d=20$) (Right).

Figure 6

The $P-m$ curves for the degenerate Bloch brane solution II (17). The parameters are set to $b=1$, $v=1$, $c_0=1/16-10^{-10}$ ($d=10$) (Left), and $c_0=1/16-10^{-20}$ ($d=20$) (Right).

Figure 7

The shapes of the resonant modes corresponding to the three peaks in Fig. 5.