Critical $N=(1,1)$ general massive supergravity

In this paper we study the supermultiplet structure of $N=(1,1)$ General Massive Supergravity at non-critical and critical points of its parameter space. To do this, we first linearize the theory around its maximally supersymmetric AdS${}_3$ vacuum and obtain the full linearized Lagrangian including fermionic terms. At generic values, linearized modes can be organized as two massless and 2 massive multiplets where supersymmetry relates them in the standard way. At critical points logarithmic modes appear and we find that in three of such points some of the supersymmetry transformations are non-invertible in logarithmic multiplets. However, in the fourth critical point, there is a massive logarithmic multiplet with invertible supersymmetry transformations.