  We obtain exact analytical solutions for a class of SO($l$) Higgs field
theories in a non-dynamic background $n$-dimensional anti de Sitter space.
These finite transverse energy solutions are maximally symmetric
$p$-dimensional topological defects where $n=(p+1)+l$. The radius of curvature
of anti de Sitter space provides an extra length scale that allows us to study
the equations of motion in a limit where the masses of the Higgs field and the
massive vector bosons are both vanishing. We call this the double BPS limit. In
anti de Sitter space, the equations of motion depend on both $p$ and $l$. The
exact analytical solutions are expressed in terms of standard special
functions. The known exact analytical solutions are for kink-like defects
($p=0,1,2,\dotsc;\, l=1$), vortex-like defects ($p=1,2,3;\, l=2$), and the
'tHooft-Polyakov monopole ($p=0;\, l=3$). A bonus is that the double BPS limit
automatically gives a maximally symmetric classical glueball type solution. In
certain cases where we did not find an analytic solution, we present numerical
solutions to the equations of motion. The asymptotically exponentially
increasing volume with distance of anti de Sitter space imposes different
constraints than those found in the study of defects in Minkowski space.
