Unitary supermultiplets of OSp(1/32, ℝ) and M-theory

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Abstract

We review the oscillator construction of the unitary representations of non-compact groups and supergroups and study the unitary supermultiplets of OSp(1/32, ℝ) in relation to M-theory. OSp(1/32, ℝ) has a singleton supermultiplet consisting of a scalar and a spinor field. Parity invariance leads us to consider OSp(1/32, ℝ)L × OSp(1/32, ℝ)R as the "minimal" generalized AdS supersymmetry algebra of M-theory corresponding to the embedding of two spinor representations of SO(10, 2) in the fundamental representation of Sp(32, ℝ). The contraction to the Poincaré superalgebra with central charges proceeds via a diagonal subsupergroup OSp(1/32, ℝ)L-R which contains the common subgroup SO(10, 1) of the two SO(10, 2) factors. The parity invariant singleton supermultiplet of OSp(1/32, ℝ)L × OSp(1/32, ℝ)R decomposes into an infinite set of "doubleton" supermultiplets of the diagonal OSp(1/32, ℝ)L-R. There is a unique "CfT self-conjugate" doubleton supermultiplet whose tensor product with itself yields the "massless" generalized AdS11 supermultiplets. The massless graviton supermultiplet contains fields corresponding to those of eleven-dimensional supergravity plus additional ones. Assuming that an AdS phase of M-theory exists we argue that the doubleton field theory must be the holographic superconformal field theory in ten dimensions that is dual to M-theory in the same sense as the duality between the N = 4 super-Yang-Mills in d = 4 and the IIB superstring over AdS5 × S5.

Original languageEnglish (US)
Pages (from-to)432-450
Number of pages19
JournalNuclear Physics B
Volume528
Issue number1-2
DOIs
StatePublished - Sep 14 1998

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parity
gravitons
subgroups
supergravity
embedding
contraction
supersymmetry
invariance
algebra
oscillators
tensors
scalars
products

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Cite this

@article{9e6c9e6047644a53a3e9499f6f36bae3,
title = "Unitary supermultiplets of OSp(1/32, ℝ) and M-theory",
abstract = "We review the oscillator construction of the unitary representations of non-compact groups and supergroups and study the unitary supermultiplets of OSp(1/32, ℝ) in relation to M-theory. OSp(1/32, ℝ) has a singleton supermultiplet consisting of a scalar and a spinor field. Parity invariance leads us to consider OSp(1/32, ℝ)L × OSp(1/32, ℝ)R as the {"}minimal{"} generalized AdS supersymmetry algebra of M-theory corresponding to the embedding of two spinor representations of SO(10, 2) in the fundamental representation of Sp(32, ℝ). The contraction to the Poincar{\'e} superalgebra with central charges proceeds via a diagonal subsupergroup OSp(1/32, ℝ)L-R which contains the common subgroup SO(10, 1) of the two SO(10, 2) factors. The parity invariant singleton supermultiplet of OSp(1/32, ℝ)L × OSp(1/32, ℝ)R decomposes into an infinite set of {"}doubleton{"} supermultiplets of the diagonal OSp(1/32, ℝ)L-R. There is a unique {"}CfT self-conjugate{"} doubleton supermultiplet whose tensor product with itself yields the {"}massless{"} generalized AdS11 supermultiplets. The massless graviton supermultiplet contains fields corresponding to those of eleven-dimensional supergravity plus additional ones. Assuming that an AdS phase of M-theory exists we argue that the doubleton field theory must be the holographic superconformal field theory in ten dimensions that is dual to M-theory in the same sense as the duality between the N = 4 super-Yang-Mills in d = 4 and the IIB superstring over AdS5 × S5.",
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Unitary supermultiplets of OSp(1/32, ℝ) and M-theory. / Günaydin, M.

In: Nuclear Physics B, Vol. 528, No. 1-2, 14.09.1998, p. 432-450.

Research output: Contribution to journalArticle

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