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.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics