Spectra of PP-Wave Limits of M-/Superstring Theory on AdSp× SqSpaces

In this paper we show how one can obtain very simply the spectra of thePP-wave limits of M-theory over AdS_7(4) x S^4(7) spaces and IIB superstringtheory over AdS_5 x S^5 from the oscillator construction of the Kaluza-Kleinspectra of these theories over the corresponding spaces. The PP-wave symmetrysuperalgebras are obtained by taking the number P of ``colors'' of oscillatorsto be large (infinite). In this large P limit, the symmetry superalgebraosp(8*|4) of AdS_7 x S^4 and the symmetry superalgebra osp(8|4,R) of AdS_4 xS^7 lead to isomorphic PP-wave algebras, which is the semi-direct sum ofsu(4|2) with H^(18,16), while the symmetry superalgebra su(2,2|4) of AdS_5 xS^5 leads to the semi-direct sum of [psu(2|2) + psu(2|2) + u(1)] with H^(16,16)as its PP-wave algebra [H^(m,n) denoting a super-Heisenberg algebra with mbosonic and n fermionic generators]. The zero mode spectra of M-theory or IIBsuperstring theory in the PP-wave limit corresponds simply to the unitarypositive energy representations of these algebras whose lowest weight vector isthe Fock vacuum of all the oscillators. General positive energy supermultipletsincluding those corresponding to higher modes can similarly be constructed bythe oscillator method.Comment: Typos corrected; references added; minor modifications to improve presentation; 37 pages, LaTeX fil