Regular compactifications and Higgs model vortices

We present full numerical solutions to the system of a global string embedded in a six-dimensional space-time. The solutions are regular everywhere and do confine gravity in our four-dimensional world. They depend on the value of the (negative) cosmological constant in the bulk and on the parameters of the Higgs potential, and we perform a systematic study to determine their allowed values. We also comment on the relation of our results with previous studies on the same subject and on their phenomenological viability.

Figure 1

Plot of $f(x)/f_{\infty }$ as a function of $x$ for $v=1$, ${\Lambda }_c=-0.0671$.

Figure 2

Plot of $L(x)/L_{\infty }$ as a function of $x$ for $v=1$, ${\Lambda }_c=-0.0671$.

Figure 3

Plot of $m(x)/m_{\infty }$ as a function of $x$ for $v=1$, ${\Lambda }_c=-0.0671$.

Figure 4

Plot of $m(x)/m_{\infty }$ as a function of $x$ for $v=1.4$, $v=1$, $v=0.7$ and $v=0.6$

Figure 5

Plot of the $(x,y)$ phase space, for $v=1$.

Figure 6

Plot of $-{\Lambda }_c/\lambda$ as a function of $v$, for small values of the latter. We have superimposed to the data the best fit we could find, given by Eq. (22) with $a=6.3$, $b=9.0$.

Figure 7

Plot of $-{\Lambda }_c/(\lambda v^4)$ as a function of $v$.