Supersymmetric multi-trace boundary conditions in AdS

Abstract

Boundary conditions for massive fermions are investigated in AdSd for d ⩾ 2. For fermion masses in the range 0 ⩽ |m| < 1/2ℓ with ℓ being the AdS length, the standard notion of normalizeability allows a choice of boundary conditions. As in the case of scalars at or slightly above the Breitenlohner–Freedman (BF) bound, such boundary conditions correspond to multi-trace deformations of any CFT dual. By constructing appropriate boundary superfields, for d = 3, 4, 5 we identify joint scalar/fermion boundary conditions which preserve either supersymmetry or superconformal symmetry on the boundary. In particular, we identify boundary conditions corresponding via AdS/CFT (at large N) to a 595-parameter family of double-trace marginal deformations of the low-energy theory of N M2-branes which preserve superconformal symmetry. We also establish that (at large N and large 't Hooft coupling λ) there are no marginal or relevant multi-trace deformations of 3+1 super Yang–Mills which preserve even supersymmetry.