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

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 $(\mathrm{\partial }\cdot J_3{)}^{QF}$ 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 $⟨J_{---}{J}_{+}{J}_{+}{J}_{+}{⟩}_{QF}$.