Confining string formed by $P$-vortices in the indirect $\mathbf{Z(2)}$ projection of $\mathbf{SU(2)}$ lattice gauge theory

We study the distribution of $P$-vortices near the confining string in the indirect $Z(2)$ projection of $SU(2)$ lattice gauge theory. We find that the density of vortices approaches the vacuum value at large distances and is strongly suppressed near the line connecting the test quark-antiquark pair. This implies that the condensate of $P$-vortices is broken inside the confining string. The width of the $P$-vortex density distribution increases with increasing distance between the quark and antiquark. Our best fit indicates the logarithmic dependence of this width on $q\bar{q}$ separation distance.