Supersymmetric multi-trace boundary conditions in AdS

Abstract

Boundary conditions for massive fermions are investigated in AdS d for d ≥ 2. For fermion masses in the range 0 ≤ |m| < 1/2ℓ with ℓ 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 BreitenlohnerFreedman (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 N = 1 supersymmetry or 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 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 N = 4 super Yang-Mills which preserve even N = 1 supersymmetry. Contents

Stability in Einstein-scalar gravity with a logarithmic branch

“…In any case, the superpotential (3.3) is non-analytic and thus would not arise in a supersymmetric theory. Furthermore, the boundary conditions that we consider do not preserve supersymmetry, and in particular, there are no supersymmetric multi-trace deformations when the BF bound is saturated [48].…”

Supersymmetric mixed boundary conditions in AdS2 and DCFT1 marginal deformations

“…We generically refer to each of them as φ and ψ respectively, and we will be particularly interested in the massless modes. For completeness we remind the reader that in AdS 2 alternative quantizations for bosons and fermions arise respectively for − 1 4 ≤ m 2 B ≤ 3 4 and |m F | ≤ 1 2 (see [5], [24]). For any complex pair of fluctuation fields, the dynamics can be obtained from the following bulk action [25],…”

Correlation functions in ω-deformed N = 6 $$ \mathcal{N}=6 $$ supergravity

“…We shall, therefore, still impose standard Dirichlet boundary conditions on the spin-3 2 and spin-2 gauge fields. With the boundary conditions for the spin-3 2 and spin-2 fields thus determined, the supersymmetry-preserving boundary conditions for the lower-spin fields can then be derived from the supersymmetry transformations of the coefficient functions associated with the large-distance expansions of the lower-spin fields [20][21][22].…”