Konishi lifts a black hole

TL;DR

The paper addresses a mismatch in one-loop BPS spectra between $SO(7)$ and $Sp(3)$ \mathcal{N}=4 SYM by showing that the classical fortuitous cohomology $O_f$ and monotone cohomology $O_m$ are lifted when quantum corrections to $Q$ are included. The authors derive a one-loop correction $Q_K$ to the supercharge from the generalized Konishi anomaly, and compute its action on $O_f$, finding $Q_K O_f \propto O_m$ up to $Q_0$-exact terms, implying $O_m$ becomes $Q$-exact in the full quantum theory. This pairing yields a long multiplet that cancels the would-be extra BPS states, supporting that the quantum cohomology respects S-duality. The results illuminate how quantum effects modify chiral ring counting and hint at broader implications for BMN sectors, non-perturbative corrections, and extensions to theories with less supersymmetry.

Abstract

We investigate the \emph{quantum} cohomology of a supercharge $Q$ in $\mathcal{N}=4$ super Yang-Mills theory. Recent analyses have revealed a mismatch between the one-loop BPS spectra of the S-dual $SO(7)$ and $Sp(3)$ theories. The $SO(7)$ theory contains a pair of additional graviton (monotone) and non-graviton (fortuitous) cohomologies, whose net contributions cancel in the superconformal index. We show that the quantum-corrected $Q$, inferred from the generalized Konishi anomaly, pairs and lifts these extra cohomologies.