Supercoherent states of , conformal superfields and the AdS7/CFT6 duality (original) (raw)
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Letters in Mathematical Physics - LETT MATH PHYS, 2000
We construct unitary representations of (1,0) and (2,0) superconformal algebras in six dimensions by using superfields defined on harmonic superspaces with coset manifolds USp(2n)/[U(1)]n, n=1, 2. In the spirit of the AdS7/CFT6 correspondence, massless conformal fields correspond to ‘supersingletons’ in AdS7. By tensoring them we produce all short representations corresponding to 1/2 and 1/4 BPS anti-de Sitter bulk states of which ‘massless bulk’ representations are particular cases.
Unitary supermultiplets of and the AdS7/CFT6 duality
Nuclear Physics B, 2000
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.
Conformal superfields and BPS states in AdS4/7AdS_{4/7}AdS4/7 geometries
2000
We carry out a general analysis of the representations of the superconformal algebras OSp(8/4,R) and OSp(8*/2N) in terms of harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). Particular attention is paid to the so-called "short multiplets". Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.
Aspects of superconformal field theories in six dimensions
Journal of High Energy Physics, 2004
We introduce the analytic superspace formalism for six-dimensional (N, 0) superconformal field theories. Concentrating on the (2, 0) theory we write down the Ward identities for correlation functions in the theory and show how to solve them. We then consider the four-point function of four energy momentum multiplets in detail, explicitly solving the Ward identities in this case. We expand the four-point function using both Schur polynomials, which lead to a simple formula in terms of a single function of two variables, and (a supersymmetric generalisation of) Jack polynomials, which allow a conformal partial wave expansion. We then perform a complete conformal partial wave analysis of both the free theory four-point function and the AdS dual four-point function. We also discuss certain operators at the threshold of the series a) unitary bound, and prove that some such operators can not develop anomalous dimensions, by finding selection rules for certain three-point functions. For those operators which are not protected, we find representations with which they may combine to become long.
Seven-dimensional De Sitter and six-dimensional conformal supersymmetries
Physics Letters B, 1983
The N-extended D = 7 De Sitter algebras UaU(4, N, H) with bosonic sector SO(6, 2) X Sp(N), describing also N-extended D = 6 superconformal symmetries are given. The quatermonic structure of real representation is described by three real quaterniomc Majorana condltlon~ We conjecture thatN = 2D = 7 De Satter supergroup UaU(4,2; Iq) describes the supersymmetries of the vacuum solutaon for D = 11 supergravity, with the space-time described by seven-dimensional De Sitter space and internal space S 4. 0.031-9163/83/0000-0000/$ 03.00
Classical and Quantum Gravity, 2000
In this paper we fill a necessary gap in order to realize the explicit comparison between the Kaluza Klein spectra of supergravity compactified on AdS 4 × X 7 and superconformal field theories living on the world volume of M2-branes. On the algebraic side we consider the superalgebra Osp(N |4) and we study the double intepretation of its unitary irreducible representations either as supermultiplets of particle states in the bulk or as conformal superfield on the boundary. On the lagrangian field theory side we construct, using rheonomy rather than superfield techniques, the generic form of an N = 2, d = 3 gauge theory. Indeed the superconformal multiplets are supposed to be composite operators in a suitable gauge theory.
N = 8 supersingleton quantum field theory
Nuclear Physics B, 1988
We quantize the N = 8 supersymmetric singleton field theory which is formulated on the boundary of the four-dimensional anti-de Sitter spacetime (ADS4). The theory has rigid OSp(8, 4) symmetry which acts as a superconformal group on the boundary of AdS 4. We show that the generators of this symmetry satisfy the full quantum OSp(8, 4) algebra. The spectrum of the theory contains massless states of all higher integer and half-integer spin which fill the irreducible representations of OSp(8, 4) with highest spin sm~ ~ = 2,4,6,.... Remarkably, these are in one-toone correspondence with the generators of Vasiliev's infinite-dimensional extended higher spin superalgebra shs(8, 4), suggesting that we may have stumbled onto a field-theoretic realization of this algebra. We also discuss the possibility of a connection between the N = 8 supersingleton theory with the eleven-dimensional supermembrane in an AdS 4 × S v background.
(2, 0) tensor multiplets and conformal supergravity in D= 6
We construct the supercurrent multiplet that contains the energy-momentum tensor of the (2, 0) tensor multiplet. By coupling this multiplet of currents to the fields of conformal supergravity, we first construct the linearized superconformal transformations rules of the (2, 0) Weyl multiplet. Next, we construct the full non-linear transformation rules by gauging the superconformal algebra OSp(8 * |4). We then use this result to construct the full equations of motion of the tensor multiplet in a conformal supergravity background. Coupling N + 5 copies of the tensor multiplet to conformal supergravity and imposing a geometrical constraint on the scalar fields which fixes the conformal symmetry, we obtain the coupling of (2, 0) Poincaré supergravity to N tensor multiplets in which the physical scalars parametrize the coset SO(N, 5)/(SO(N) × SO(5)).
All positive energy unitary irreducible representations of extended conformal supersymmetry
Physics Letters B, 1985
We give the list of all positive energy UIR's of the conformal superalgebra su(2, 2/N). They are realized as subrepresentations of elementary representations. The latter are induced from irreducible finite-dimensional Lorentz and su(N) representations on spaces of functions (superfields). Some of the unitary representation spaces are comprised from solutions of invariant differential equations. Among these the massless UIR's are discussed