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We obtain exact analytical solutions for a class of SO($l$) Higgs fieldtheories 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 curvatureof anti de Sitter space provides an extra length scale that allows us to studythe equations of motion in a limit where the masses of the Higgs field and themassive vector bosons are both vanishing. We call this the double BPS limit. Inanti de Sitter space, the equations of motion depend on both $p$ and $l$. Theexact analytical solutions are expressed in terms of standard specialfunctions. 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 limitautomatically gives a maximally symmetric classical glueball type solution. Incertain cases where we did not find an analytic solution, we present numericalsolutions to the equations of motion. The asymptotically exponentiallyincreasing volume with distance of anti de Sitter space imposes differentconstraints than those found in the study of defects in Minkowski space.

Some Exact Solutions for Maximally Symmetric Topological Defects in Anti de Sitter Space