### 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 AdS_{11} 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 AdS_{5} × S^{5}.

Original language | English (US) |
---|---|

Pages (from-to) | 432-450 |

Number of pages | 19 |

Journal | Nuclear Physics B |

Volume | 528 |

Issue number | 1-2 |

DOIs | |

State | Published - Sep 14 1998 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*528*(1-2), 432-450. https://doi.org/10.1016/S0550-3213(98)00393-9

}

*Nuclear Physics B*, vol. 528, no. 1-2, pp. 432-450. https://doi.org/10.1016/S0550-3213(98)00393-9

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Unitary supermultiplets of OSp(1/32, ℝ) and M-theory

AU - Günaydin, M.

PY - 1998/9/14

Y1 - 1998/9/14

N2 - 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.

AB - 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.

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U2 - 10.1016/S0550-3213(98)00393-9

DO - 10.1016/S0550-3213(98)00393-9

M3 - Article

AN - SCOPUS:0032517020

VL - 528

SP - 432

EP - 450

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -