### Abstract

In this paper we show how one can obtain very simply the spectra of the PP-wave limits of M-theory over AdS_{7(4)} × S^{4(7)} spaces and IIB superstring theory over AdS_{5} × S^{5} from the oscillator construction of the Kaluza-Klein spectra of these theories over the corresponding spaces. The PP-wave symmetry superalgebras are obtained by taking the number P of "colors" of oscillators to be large (infinite). In this large P limit, the symmetry superalgebra osp(8*|4) of AdS_{7} × S^{4} and the symmetry superalgebra osp(8|4, ℝ) of AdS_{4} × S^{7} lead to isomorphic PP-wave algebras, which is su(4|2) hook sign^{18,16}, while the symmetry superalgebra su(2, 2|4) of AdS_{5} × S^{5} leads to [psu(2|2) ⊕ psu(2|2) ⊕ u(1)] S inside a circle sign hook sign ^{16,16} as its PP-wave algebra [hook sign^{m, n} denoting a super-Heisenberg algebra with m bosonic and n fermionic generators]. The zero mode spectra of M-theory or IIB superstring theory in the PP-wave limit correspond simply to the unitary positive energy representations of these algebras whose lowest weight vector is the Fock vacuum of all the oscillators. General positive energy supermultiplets including those corresponding to higher modes can similarly be constructed by the oscillator method.

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

Pages (from-to) | 129-163 |

Number of pages | 35 |

Journal | Journal of High Energy Physics |

Volume | 6 |

Issue number | 10 |

State | Published - Oct 1 2002 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

_{p}× S

^{q}spaces.

*Journal of High Energy Physics*,

*6*(10), 129-163.

}

_{p}× S

^{q}spaces',

*Journal of High Energy Physics*, vol. 6, no. 10, pp. 129-163.

**Spectra of PP-wave limits of M-/Superstring theory on AdS _{p} × S^{q} spaces.** / Fernando, Sudarshan; Gunaydin, Murat; Pavlyk, Oleksandr.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Spectra of PP-wave limits of M-/Superstring theory on AdSp × Sq spaces

AU - Fernando, Sudarshan

AU - Gunaydin, Murat

AU - Pavlyk, Oleksandr

PY - 2002/10/1

Y1 - 2002/10/1

N2 - In this paper we show how one can obtain very simply the spectra of the PP-wave limits of M-theory over AdS7(4) × S4(7) spaces and IIB superstring theory over AdS5 × S5 from the oscillator construction of the Kaluza-Klein spectra of these theories over the corresponding spaces. The PP-wave symmetry superalgebras are obtained by taking the number P of "colors" of oscillators to be large (infinite). In this large P limit, the symmetry superalgebra osp(8*|4) of AdS7 × S4 and the symmetry superalgebra osp(8|4, ℝ) of AdS4 × S7 lead to isomorphic PP-wave algebras, which is su(4|2) hook sign18,16, while the symmetry superalgebra su(2, 2|4) of AdS5 × S5 leads to [psu(2|2) ⊕ psu(2|2) ⊕ u(1)] S inside a circle sign hook sign 16,16 as its PP-wave algebra [hook signm, n denoting a super-Heisenberg algebra with m bosonic and n fermionic generators]. The zero mode spectra of M-theory or IIB superstring theory in the PP-wave limit correspond simply to the unitary positive energy representations of these algebras whose lowest weight vector is the Fock vacuum of all the oscillators. General positive energy supermultiplets including those corresponding to higher modes can similarly be constructed by the oscillator method.

AB - In this paper we show how one can obtain very simply the spectra of the PP-wave limits of M-theory over AdS7(4) × S4(7) spaces and IIB superstring theory over AdS5 × S5 from the oscillator construction of the Kaluza-Klein spectra of these theories over the corresponding spaces. The PP-wave symmetry superalgebras are obtained by taking the number P of "colors" of oscillators to be large (infinite). In this large P limit, the symmetry superalgebra osp(8*|4) of AdS7 × S4 and the symmetry superalgebra osp(8|4, ℝ) of AdS4 × S7 lead to isomorphic PP-wave algebras, which is su(4|2) hook sign18,16, while the symmetry superalgebra su(2, 2|4) of AdS5 × S5 leads to [psu(2|2) ⊕ psu(2|2) ⊕ u(1)] S inside a circle sign hook sign 16,16 as its PP-wave algebra [hook signm, n denoting a super-Heisenberg algebra with m bosonic and n fermionic generators]. The zero mode spectra of M-theory or IIB superstring theory in the PP-wave limit correspond simply to the unitary positive energy representations of these algebras whose lowest weight vector is the Fock vacuum of all the oscillators. General positive energy supermultiplets including those corresponding to higher modes can similarly be constructed by the oscillator method.

UR - http://www.scopus.com/inward/record.url?scp=23044495040&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044495040&partnerID=8YFLogxK

M3 - Article

VL - 6

SP - 129

EP - 163

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 10

ER -

_{p}× S

^{q}spaces. Journal of High Energy Physics. 2002 Oct 1;6(10):129-163.