Fortuity and relevant deformation

A bstract We investigate the supercharge cohomology of an 𝒩 = 1 relevant deformation of 𝒩 = 4 super Yang-Mills. By introducing a field redefinition, we integrate out massive fields in a cohomological sense. Then, we construct the monotone cohomologies corresponding to the Kaluza-Klein particles of the dual supergravity solution. Some of the monotone cohomologies obey stringy exclusion principle analogous to that of AdS 3 . Relatedly, they vanish on the diagonal field configurations, unlike 𝒩 = 4 monotone cohomologies. We also construct infinitely many fortuitous cohomologies for gauge group SU(2). We find that unlike 𝒩 = 4 fortuitous cohomologies, they can either be non-vanishing or vanishing on the diagonal fields. By undoing the field redefinition and taking a suitable UV limit, we show that non-vanishing ones reduce to monotone cohomologies of 𝒩 = 4 SYM, while vanishing ones reduce to fortuitous cohomologies of 𝒩 = 4 SYM. This implies that the fortuity can arise due to the relevant deformation, while monotonicity does not.