Supergravitons from one loop perturbative N=4 SYM

TL;DR

The authors determine the partition function for $1/16$ BPS operators in ${ m  N=4}$ SYM at weak coupling in the planar limit by implementing Beisert's oscillator-based one-loop dilatation operator. They identify states with zero one-loop anomalous dimension and construct generating functions for fixed length, then sum to obtain the full single- and multi-trace partition functions. A key result is an exact match between the one-loop gauge theory partition function and the $1/16$ BPS supergraviton partition function in ${ m AdS}_5 imes { m S}^5$, implying a precise gauge/gravity correspondence for this sector at this perturbative order. The analysis also highlights that black-hole-like entropy scaling $oldsymbol{ log Z} sim N^2$ likely requires nonplanar dynamics beyond the one-loop planar calculation, suggesting the need for nonplanar dilatation operators or higher-loop effects to access the full thermodynamic behavior. Overall, the work demonstrates a clean, combinatorial agreement between weakly coupled gauge theory and its gravity dual in a nontrivial BPS sector and clarifies the role of planarity in the counting of such states.

Abstract

We determine the partition function of 1/16 BPS operators in N=4 SYM at weak coupling at the one-loop level in the planar limit. This partition function is significantly different from the one computed at zero coupling. We find that it coincides precisely with the partition function of a gas of 1/16 BPS `supergravitons' in AdS_5xS^5.