Spectra of PP-Wave Limits of M-/Superstring Theory on AdS_p x S^q Spaces

TL;DR

This paper derives the spectra of PP-wave limits of M-theory and superstring theory on AdS x S spaces using oscillator methods, revealing algebraic structures and spectra in the large oscillator number limit.

Contribution

It provides a simple oscillator-based method to obtain spectra of PP-wave limits from known Kaluza-Klein spectra, connecting superalgebras in the large P limit.

Findings

Spectra of PP-wave limits derived from oscillator construction.

Identification of isomorphic superalgebras in large P limit.

Zero mode spectra correspond to unitary positive energy representations.

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) x S^4(7) spaces and IIB superstring theory over AdS_5 x 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 x S^4 and the symmetry superalgebra osp(8|4,R) of AdS_4 x S^7 lead to isomorphic PP-wave algebras, which is the semi-direct sum of su(4|2) with H^(18,16), while the symmetry superalgebra su(2,2|4) of AdS_5 x S^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 m bosonic and n fermionic generators]. The zero mode spectra of M-theory or IIB superstring theory in the PP-wave limit corresponds 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.