1/16 BPS States in N=4 SYM

TL;DR

The paper tackles counting 1/16 BPS operators in N=4 SYM at weak coupling by recasting the problem as Q-cohomology on gauge-invariant words and formulating it in terms of relative Lie algebra cohomology of an infinite-dimensional algebra. It derives a complete Q-cohomology set at infinite N that matches free multi-graviton states in AdS5×S5 and conjectures that all 1/16 BPS operators are of multi-graviton form, supported by numerical checks in small N. At finite N, it computes implications for the refined index and finds that the multi-graviton sector underpredicts the entropy of large 1/16 BPS black holes, posing a puzzle about coupling dependence or the existence of such black holes in string theory. The work highlights a tension between weak-coupling BPS counting and bulk black hole entropy, suggesting potential resolutions involving coupling effects or the structure of high-energy microstates.

Abstract

We investigate the problem of counting 1/16 BPS operators in N=4 Super-Yang-Mills theory at weak coupling. We present the complete set of 1/16 BPS operators in the infinite N limit, which agrees with the counting of free BPS multi-graviton states in the gravity dual AdS5xS5. Further, we conjecture that all 1/16 BPS operators in N=4 SYM are of the multi-graviton form, and give numerical evidences for this conjecture. We discuss the implication of our conjecture and the seeming failure in reproducing the entropy of large 1/16 BPS black holes in AdS5.