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 $\lambda$) 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

References in corpus (26)

• Gauge Theory Correlators from Non-Critical String Theory
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• AdS/CFT Correspondence and Symmetry Breaking
• Setting the boundary free in AdS/CFT
• Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
• Spinors and the AdS/CFT correspondence
• "Double-trace" Deformations, Boundary Conditions and Spacetime Singularities
• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields
• Designer Gravity and Field Theory Effective Potentials
• Double-trace operators and one-loop vacuum energy in AdS/CFT
• Particle-Like Solutions of the Einstein-Dirac Equations
• On the origin of supergravity boundary terms in the AdS/CFT correspondence
• A Note on Multi-trace Deformations and AdS/CFT
• Energy Bounds in Designer Gravity
• Supersymmetric spacetimes in 2+1 adS-supergravity models
• Rigid supersymmetry with boundaries
• Consistent boundary conditions for supergravity
• Killing spinors and Supersymmetry on AdS
• Matter Coupled AdS_3 Supergravities and Their Black Strings
• The Dirac particle on central backgrounds and the anti-de Sitter oscillator
• Comments on Cosmic Censorship in AdS/CFT
• Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry
• Discrete quantum modes of the Dirac field in $Ad{S}_{d+1}$ backgrounds
• Reversing Renormalization-Group Flows with AdS/CFT
• (2,0) Chern-Simons Supergravity Plus Matter Near the Boundary of AdS_3

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