PP Wave Limit and Enhanced Supersymmetry in Gauge Theories

TL;DR

The paper shows that the pp‑wave limit of AdS5×M^5 backgrounds with smooth Sasaki–Einstein M^5 is universal and yields maximal supersymmetry, enabling a BMN‑type mapping between large R‑charge gauge theory operators and light‑cone string oscillators. Focusing on AdS5×T^{1,1} (N=1) and a Z2 orbifold of S^5 (N=2), it demonstrates how the Penrose limit reveals enhanced subsectors in the gauge theories, and it constructs explicit, protected and near‑protected operator sets corresponding to the string spectrum, including twisted and untwisted sectors. It also identifies exact expressions for the light‑cone Hamiltonian and its spectrum, showing how large‑N, large‑t Hooft coupling control the matching and where alpha′ corrections may appear away from the strict limit. The results illuminate how supersymmetry can be effectively enhanced in high‑charge sectors and provide concrete operator dictionaries linking gauge theory dynamics to string excitations in pp‑wave backgrounds with and without orbifold singularities, with implications for non‑maximally supersymmetric holography.

Abstract

We observe that the pp wave limit of $AdS_5\times M^5$ compactifications of type IIB string theory is universal, and maximally supersymmetric, as long as $M^5$ is smooth and preserves some supersymmetry. We investigate a specific case, $M^5=T^{1,1}$. The dual ${\cal N}=1$ SCFT, describing D3-branes at a conifold singularity, has operators that we identify with the oscillators of the light-cone string in the universal pp-wave background. The correspondence is remarkable in that it relies on the exact spectrum of anomalous dimensions in this CFT, along with the existence of certain exceptional series of operators whose dimensions are protected only in the limit of large `t Hooft coupling. We also briefly examine the singular case $M^5=S^5/Z_2$, for which the pp wave background becomes a $Z_2$ orbifold of the maximally supersymmetric background by reflection of 4 transverse coordinates. We find operators in the corresponding ${\cal N}=2$ SCFT with the right properties to describe both the untwisted and the twisted sectors of the closed string.