Year: 2026
Type: preprint
Abstract: We study quantum lifting of classical $Q$-cohomology classes in four-dimensional $\mathcal{N}=4$ super-Yang--Mills theory. Certain powers of the gaugino bilinear $\mathcal{S}=\text{Tr}(λ_+λ_-)$ in orthogonal theories provide non-Coulomb monotones: multi-graviton classes that vanish upon Cartan restriction. For $SO(7)$, we identify $\mathcal S^4$ as a superconformal descendant of a known lifted monotone class, explaining the latter's non-Coulomb character. We explicitly construct a fortuitous lifting partner for $\mathcal S^4$ that is, by contrast, visible on the Coulomb branch. This construction provides a strategy for finding analogous partners for higher powers at higher ranks. Our main result establishes restrictions on quantum lifting in the multi-trace sector of the classical gauge-group families. We show that the one-loop correction $Q_1$ to the supercharge annihilates every monotone class in classical cohomology, while every $[Q_1]$ image has vanishing Cartan restriction. Thus every non-zero one-loop pairing has a fortuitous source and a non-Coulomb target, and Coulomb monotones survive at this order at finite rank. In the BMN sector, our results imply that non-Coulomb monotones also survive at one loop. A crucial step shows that dressing any classical class by a sufficiently high power of a scalar discriminant yields a multi-graviton class, or zero in cohomology when the original class is non-Coulomb. We interpret this annihilation as a partial no-hair property.
Source: arXiv (Cornell University)
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G1361613305
OpenAlex ID: W7222714178