Supercoherent states of , conformal superfields and the AdS7/CFT6 duality (original) (raw)

Abstract

We study the positive energy unitary representations of 2N extended superconformal algebras OSp(8 * |2N) in six dimensions. These representations can be formulated in a particle basis or a supercoherent state basis, which are labeled by the superspace coordinates in d = 6. We show that the supercoherent states that form the bases of positive energy representations of OSp(8 * |2N) can be identified with conformal superfields in six dimensions. The massless conformal superfields correspond precisely to the ultra short doubleton supermultiplets of OSp(8 * |2N). The other positive energy unitary representations correspond to massive conformal superfields in six dimensions and they can be obtained by tensoring an arbitrary number of doubleton supermultiplets with each other. The supermultiplets obtained by tensoring two copies of the doubletons correspond to massless anti-de Sitter supermultiplets in d = 7.

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References (56)

  1. N = 2, the shortest such supermultiplet is the massless AdS graviton supermultiplet of OSp(8 * |4). We give the explicit expression for the corresponding supercoherent state in Section 4.2. We conclude with a discussion of our results.
  2. 2 Coherent states of the positive energy unitary representations of the group SO * (8) and conformal fields in six dimensions The commutation relations of the generators of the conformal group SO(6, 2) in d = 6, which is isomorphic to SO * (8), can be written as [M µν , M ρσ ] = i(η νρ M µσ -η µρ M νσ -η νσ M µρ + η µσ M νρ ), [P µ , M ρσ ] = i(η µρ P σ -η µσ P ρ ), [K µ , M ρσ ] = i(η µρ K σ -η µσ K ρ ), [D, M µν ] = [P µ , P ν ] = [K µ , K ν ] = 0, [P µ , D] = iP µ , [K µ , D] = -iK µ , [P µ , K ν ] = 2i(η µν D -M µν ), (2 -1) References
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