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arXiv · 0808.2184

Supersymmetric Multi-trace Boundary Conditions in AdS

Aaron J. Amsel·Donald Marolf
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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 $λ$) 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.

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Aaron J. Amsel, Donald Marolf. 2008-11-22. Supersymmetric Multi-trace Boundary Conditions in AdS. https://doi.org/10.1088/0264-9381%2F26%2F2%2F025010

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