Four-point functions and contact terms from higher-spin Ward identities of Chern-Simons-matter theory

A bstract Large N quasifermionic ( QF ) Chern-Simons-matter theories exhibit weakly-broken higher-spin symmetry and contain an infinite-dimensional algebra of almost-conserved higher-spin currents. By analyzing local higher-spin Ward identities, we constrain the higher-spin algebra of this theory, for operators of spin s < 4. The solution interpolates smoothly between Ward identities of free-fermionic and critical-bosonic U( N ) models, in accordance with the bosonization duality. At finite ’t Hooft coupling, we decompose four-point current correlators involving (∂ ∙ J 3 ) QF in terms of free theory structures and identify possible epsilon-transform relations for QF four-point functions. Additionally, we find that higher correlators of the theory develop scheme-independent higher-spin contact terms, stemming from the presence of a background Chern-Simons term in the effective action. These terms are related to similar contact terms of the associated quasibosonic Chern-Simons-matter theory via Legendre transform. The results are supplemented by perturbative checks, including collinear limit computations of ⟨ T − − J + J + ⟩ QF , ⟨ T − − J + J + O ⟩ QF and ⟨ J − − − J + J + J + ⟩ QF .