Supersymmetric Multi-trace Boundary Conditions in AdS

• Published in: arXiv.org
• Main Authors: Amsel, Aaron J, Marolf, Donald
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 22.11.2008
• Subjects: Boundary conditions; Branes; Deformation; Energy theory; Fermions; Physics - General Relativity and Quantum Cosmology; Physics - High Energy Physics - Theory; Scalars; Supersymmetry; Symmetry
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0808.2184

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.