Stability of the Bragg glass phase in a layered geometry

We study the stability of the dislocation-free Bragg glass phase in a layered geometry consisting of coupled parallel planes of d=1+1 vortex lines lying within each plane, in the presence of impurity disorder. Using renormalization group, replica variational calculations and physical arguments we show that at temperatures $T<T_G$ the 3D Bragg glass phase is always stable for weak disorder. It undergoes a weakly first order transition into a decoupled 2D vortex glass upon increase of disorder.