Supersymmetric Multi-trace Boundary Conditions in AdS

TL;DR

This paper investigates supersymmetric boundary conditions for fermions in AdS spaces, identifying conditions that preserve supersymmetry and superconformal symmetry, and explores their implications for dual conformal field theories and deformations.

Contribution

It constructs supersymmetric boundary conditions for fermions in AdS, linking them to multi-trace deformations in dual CFTs, and analyzes their preservation of supersymmetry.

Findings

Identifies boundary conditions preserving ${ m N}=1$ supersymmetry or superconformal symmetry.

Connects boundary conditions to a 595-parameter family of double-trace deformations in M2-brane theories.

Shows no marginal or relevant multi-trace deformations preserve ${ m N}=1$ supersymmetry in ${ m N}=4$ super Yang-Mills.

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 ${\cal N}=1$ supersymmetry or ${\cal N}=1$ 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 ${\cal N} =1$ superconformal symmetry. We also establish that (at large N and large 't Hooft coupling $\lambda$) there are no marginal or relevant multi-trace deformations of 3+1 ${\cal N} =4$ super Yang-Mills which preserve even ${\cal N}=1$ supersymmetry.