PP Wave Limit and Enhanced Supersymmetry in Gauge Theories

TL;DR

This paper explores the universal nature of the pp wave limit in certain string theory backgrounds, revealing enhanced supersymmetry and linking it to dual gauge theories with protected operator spectra.

Contribution

It demonstrates the universality of the pp wave limit in $AdS_5\times M^5$ compactifications and identifies dual operators in ${\cal N}=1$ and ${\cal N}=2$ SCFTs, including cases with orbifold singularities.

Findings

The pp wave limit is maximally supersymmetric for smooth $M^5$.

Operators in the dual SCFTs match string oscillators in the pp wave background.

Protected operator dimensions are identified in the large 't Hooft coupling limit.

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.