Spectra of PP-wave limits of M-/Superstring theory on AdS_p × S^q spaces

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 sign^18,16, 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 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.