  We construct numerically gravitational duals of theories deformed by
localized Dirac delta sources for scalar operators both at zero and at finite
temperature. We find that requiring that the backreacted geometry preserves the
original scale invariance of the source uniquely determines the potential for
the scalar field to be the one found in a certain Kaluza-Klein compactification
of $11D$ supergravity. This result is obtained using an efficient perturbative
expansion of the backreacted background at zero temperature and is confirmed by
a direct numerical computation. Numerical solutions at finite temperatures are
obtained and a detailed discussion of the numerical approach to the treatment
of the Dirac delta sources is presented. The physics of defect configurations
is illustrated with a calculation of entanglement entropy.
