Fortuity in ABJM

A

bstract

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

= 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

$$ \mathcal{N} $$ 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.