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

Abstract

Abstract 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 .

Keywords

• Higher Spin Symmetry
• Chern-Simons Theories
• 1/N Expansion
• Higher Spin Gravity