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

TL;DR

This paper explores higher-spin Ward identities in large N Chern-Simons-matter theories, revealing contact terms and dualities that connect free and interacting models through algebraic and perturbative analyses.

Contribution

It derives constraints on higher-spin algebra, identifies scheme-independent contact terms, and demonstrates their relation via Legendre transform, advancing understanding of dualities in Chern-Simons-matter theories.

Findings

Higher-spin Ward identities constrain operator algebra.

Scheme-independent contact terms are identified in correlators.

Results support bosonization duality and include perturbative checks.

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 $(\partial\cdot J_3)^{QF}$ 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 $\langle T_{--}J_+J_+\rangle_{QF}$, $\langle T_{--}J_+J_+O\rangle_{QF}$ and $\langle J_{-{}-{}-}J_+J_+J_+\rangle_{QF}$.