We present a supersymmetric version of the two-brane Randall-Sundrum scenario, with arbitrary brane tensions T 1 and T 2 , subject to the bound |T 1,2 | ≤ √ −6Λ 5 , where Λ 5 < 0 is the bulk cosmological constant. Dimensional reduction gives N = 1, D = 4 supergravity, with cosmological constant Λ 4 in the range 1 2 Λ 5 ≤ Λ 4 ≤ 0. The case with Λ 4 = 0 requires T 1 = −T 2 = √ −6Λ 5 . This work unifies and generalizes previous approaches to the supersymmetric Randall-Sundrum scenario. It also shows that the Randall-Sundrum fine-tuning is not a consequence of supersymmetry.
We construct rigidly supersymmetric bulk-plus-boundary actions, both in x-space and in superspace. For each standard supersymmetric bulk action a minimal supersymmetric bulk-plus-boundary action follows from an extended F -or D-term formula. Additional separately supersymmetric boundary actions can be systematically constructed using co-dimension one multiplets (boundary superfields). We also discuss the orbit of boundary conditions which follow from the Euler-Lagrange variational principle.
We explain why it is necessary to use boundary conditions in the proof of supersymmetry of a supergravity action on a manifold with boundary. Working in both boundary ("downstairs") and orbifold ("upstairs") pictures, we present a bulk-plus-boundary/brane action for the five-dimensional (on-shell) supergravity which is supersymmetric with the use of fewer boundary conditions than were previously employed. The required Gibbons-Hawkinglike Y -term and many other aspects of the boundary/orbifold picture correspondence are discussed. * Present address: DESY-T, Notkestrasse 85, 22603 Hamburg, Germany 1 The spinors ΨMi and Hi are symplectic Majorana (see Appendix A). The index i can be rotated by Ui j ∈ SU (2): Ψ ′ i = Ui j Ψj. The (global) SU (2) is the automorphism symmetry group of the algebra when λ q = 0. The real vector q = (q1, q2, q3) indicates which U (1) subgroup of the SU (2) has been gauged [16,7]. One can set it to be a unit vector, q 2 = 1. 2 The algebra closes exactly only on the bosonic fields e A M and BM . For the gravitino, ΨMi, additional non-closure terms appear, proportional to its equation of motion. For the off-shell supersymmetry algebra see Ref. [18].
Using the simple setting of 3D N = 1 supergravity, we show how the tensor calculus of supergravity can be extended to manifolds with boundary. We present an extension of the standard F -density formula which yields supersymmetric bulk-plus-boundary actions. To construct additional separately supersymmetric boundary actions, we decompose bulk supergravity and bulk matter multiplets into co-dimension one submultiplets. As an illustration we obtain the supersymmetric extension of the York-Gibbons-Hawking extrinsic curvature boundary term. We emphasize that our construction does not require any boundary conditions on off-shell fields. This gives a significant improvement over the existing orbifold supergravity tensor calculus.
The low-energy effective action for the N = 4 super Yang-Mills on the Coulomb branch is known to include an SO(6)-invariant Wess-Zumino (WZ) term for the six scalar fields. For each maximal, non-anomalous subgroup of the SU (4) R-symmetry, we find a four-dimensional form of the WZ term with this subgroup being manifest. We then show that a recently proposed expression for the four-derivative part of the effective action in N = 4 U Sp(4) harmonic superspace yields the WZ term with manifest SO(5) R-symmetry subgroup. The N = 2 SU (2) harmonic superspace form of the effective action produces the WZ term with manifest SO(4) × SO(2). We argue that there is no four-dimensional form of the WZ term with manifest SU (3) R-symmetry, which is relevant for N = 1 and N = 3 superspace formulations of the effective action.
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