Supersymmetric Multi-trace Boundary Conditions in AdS

Abstract

Boundary conditions for massive fermions are investigated in AdS_d for $d\ge 2$. For fermion masses in the range $0\le |m|<1/2\ell$ with $\ell$ 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 $\mathcal{N}=1$ supersymmetry or $\mathcal{N}=1$ 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 $\mathcal{N}=1$ superconformal symmetry. We also establish that (at large N and large 't Hooft coupling $\hat{I}»$) there are no marginal or relevant multi-trace deformations of 3+1 $\mathcal{N}=4$ super Yang-Mills which preserve even $\mathcal{N}=1$ supersymmetry.

23 pages, 1 figure, RevTex; v2: reference added