Fortuity in ABJM

TL;DR

This paper investigates special BPS states and a fortuitous mechanism in ABJM theory, revealing new states at weak and strong coupling, especially at small quantum numbers, and proposes a non-renormalization conjecture for cohomologies.

Contribution

It provides explicit constructions of fortuitous states in ABJM at N=1 and N=2, including novel states at strong coupling and small quantum numbers, and introduces a non-renormalization conjecture.

Findings

Fortuitous states exist at N=1 and N=2 in ABJM.

Additional fortuitous states appear at k=2 in non-trivial monopole sectors.

Fortuitous states are found at smaller quantum numbers compared to N=4 SYM.

Abstract

We study $1/12$-BPS and $1/16$-BPS cohomologies and the fortuitous mechanism in ABJM theory. We first establish the existence of fortuitous states in the $N=1$ theory, where the theory is abelian and trace relations are extreme. We then provide explicit constructions of fortuitous states at $N=2$. We find fortuitous states both at weak coupling, in direct parallel to what has been done in $\mathcal{N}=4$ SYM, but we also find additional fortuitous states at $k=2$, which is in the strongly coupled regime. The extra fortuitous states that appear at $k=2$ are in non-trivial monopole sectors. A striking distinction from $\mathcal{N}=4$ SYM is that the fortuitous states appear at much smaller quantum numbers, making them easier to find. Along the way, we formulate a non-renormalization conjecture for cohomologies in ABJM.