Erratum to: “Unitary supermultiplets of OSp(8*|4) and the AdS

Abstract

We study the unitary supermultiplets of the N = 4 d = 7 anti-de Sitter (AdS 7 ) superalgebra OSp(8 * |4), with the even subalgebra SO(6, 2) × U Sp(4), which is the symmetry superalgebra of M-theory on AdS 7 × S 4 . We give a complete classification of the positive energy doubleton and massless supermultiplets of OSp(8 * |4). The ultra-short doubleton supermultiplets do not have a Poincaré limit in AdS 7 and correspond to superconformal field theories on the boundary of AdS 7 which can be identified with d = 6 Minkowski space. We show that the six dimensional Poincare mass operator m 2 = P µ P µ vanishes identically for the doubleton representations. By going from the compact U (4) basis of SO * (8) = SO(6, 2) to the noncompact basis SU * (4)×D (d = 6 Lorentz group times dilatations) one can associate the positive (conformal) energy representations of SO * (8) with conformal fields transforming covariantly under the Lorentz group in d = 6. The oscillator method used for the construction of the unitary supermultiplets of OSp(8 * |4) can be given a dynamical realization in terms of chiral super-twistor fields. CERN-TH/99-347 November, 1999 1 Work supported in part by the National Science Foundation under Grant Number PHY-9802510 2 e-mail: murat@phys.psu.edu 3 e-mail: takemae@phys.psu.edu. IntroductionRecently, a great deal of work has been done on AdS/CFT (anti-de Sitter/conformal field theory) dualities in various dimensions. The current interest in AdS/CFT dualities was sparked by the conjecture of Maldacena [1] relating the large N limits of certain conformal field theories in d dimensions to M-theory/string theory compactified to d+1-dimensional AdS spacetimes. Maldacena's conjecture was based on earlier work on properties of the physics of N Dp-branes in the near horizon limit [2] and the much earlier work on 10-d IIB supergravity compactified on AdS 5 × S 5 and 11-d supergravity compactified on AdS 7 × S 4 and AdS 4 × S 7 [3,4,5,6,7,8,9]. Maldacena's conjecture was formulated in a more precise manner in [10,11]. The relation between Maldacena's conjecture and the dynamics of the singleton and doubleton fields that live on the boundary of AdS spacetimes was reviewed in [12,13] and its relation to the spectra of maximal supergravities in eleven and ten dimensions in [13,14]. For a recent review of AdS/CFT dualities and an extensive list of references on the subject see [15].The best studied example of this AdS/CFT duality is the duality between the large N limit of the conformally invariant N = 4 SU (N ) super Yang-Mills theory in d = 4 and type IIB superstring theory on AdS 5 ×S 5 . The N = 4 Yang-Mills supermultiplet is simply the unique CPT self-conjugate doubleton supermultiplet of the symmetry superalgebra SU (2, 2|4) of type IIB superstring over AdS 5 × S 5 [4,16]. Doubleton supermultiplets do not have a smooth Poincaré limit in d = 5 and correspond to superconformal field theories on the boundary of AdS 5 , which can be identified with the four dimensional Minkowski space. The SU (2, 2|4) alg...

Minimal unitary representation of 5d superconformal algebra F(4) and AdS6Fernando1, Günaydın2 2015Nuclear Physics B

“…A 3-grading of f(4) with respect to the compact subsuperalgebra osp(2|4) ⊕ u(1) is given in Section 11, and the supermultiplet of conformal fields corresponding to the minrep of f(4) is given in Section 12. Then in Section 13, we show that the Joseph ideal vanishes identically as an operator for the minrep of SO (5,2) and hence its universal enveloping algebra yields directly the bosonic AdS 6 /CFT 5 higher spin algebra. Similarly for the deformed minrep of SO(5, 2) a certain deformation of the Joseph ideal vanishes identically and its enveloping algebra yields a deformed AdS 6 /CFT 5 higher spin algebra.…”

“…This infinite family of unitary irreducible representations of SO * (8) are isomorphic to the doubleton irreps of SO * (8) constructed in Refs. [4,5] using covariant twistorial oscillators. These results were also extended to six-dimensional conformal supergroups OSp(8 * |2N) with the even subgroup SO * (8) × USp(2N) in Ref.…”

“…We then study the minimal unitary realization of the unique simple conformal supergroup F (4) with the even subgroup SO(5, 2) × SU (2). We find that the spinor minrep, together with two copies of the scalar minrep of SO (5,2), form the minimal unitary supermultiplet of F (4). We then extend these results to the construction of AdS 6 /CFT 5 algebras and superalgebra.…”

“…In Section 2, we construct the geometric realization of SO(5, 2) as a quasiconformal group, following the method outlined in [17]. Then in Section 3, we obtain the minimal unitary representation of SO (5,2) via the quantization of the geometric quasiconformal action and show that there is a two-parameter family of degree two polynomials of so (5,2) generators that reduces to a c-number according to Joseph's theorem [18]. We present the 3-grading of so(5, 2) with respect to the noncompact subalgebra so(4, 1) ⊕ so(1, 1) in Section 4, 1 By an abuse of notation sometimes we shall use F (4) to denote both the supergroup as well as its superalgebra f (4) with the even subalgebra so(5, 2) ⊕ su (2).…”

“…Then in Section 6 we discuss the properties of a distinguished SU(1, 1) subgroup of SO (5,2) generated by singular (isotonic) oscillators. We then give the K-type decomposition of the minrep of SO (5,2) in Section 7 and show that it corresponds to a massless conformal scalar field in five dimensions. We study the deformations of the minrep in Section 8 and show that it admits a unique deformation and give its K-type decomposition in Section 9.…”