Light-Front Bootstrap for Chern-Simons Matter Theories

TL;DR

Develops a light-front bootstrap for 3d CFTs realized as Chern-Simons matter theories, using a nonlinear realization of so(3,2) built from single-trace currents. Through AdS$_4$/CFT$_3$ techniques, propagators, and a bulk-boundary dictionary, it derives all independent three-point structures and fixes their cubic couplings via algebra closure, revealing both holomorphic and anti-holomorphic sectors. The framework reproduces the known even/odd CS-matter structures and confirms 3d bosonization at leading order, while also uncovering two non-unitary chiral higher-spin gravity solutions. Additionally, it provides the complete cubic action of AdS$_4$ Higher Spin Gravity, offering a concrete bulk dual for these vector-model CFTs and clarifying the role of slightly-broken higher spin symmetry in 3d dualities.

Abstract

We propose a new approach to solve conformal field theories and apply it to Chern-Simons Matter theories and three-dimensional bosonization duality. All three-point correlation functions of single-trace operators are obtained in the large-$N$ as a simple application. The idea is to construct, as an effective weakly-coupled theory, a nonlinear realization of the conformal algebra in terms of physical, gauge-invariant, operators. The efficiency of the method is also in the use of an analog of the light-cone gauge and of the momentum-space on the CFT side. AdS/CFT is used as a convenient regulator and as a source of the canonical bracket. The uniqueness of the nonlinear realization manifests the three-dimensional bosonization duality at this order. We also find two more non-unitary solutions which should be analogous to the fishnet theories. The results can also be viewed as an explicit realization of the slightly-broken higher spin symmetry. As a by-product, the cubic action of the Higher Spin Gravity in $AdS_4$ is constructed. While generic Higher Spin Gravities are obstructed at higher orders by nonlocality, we point out the existence of two especially simple and well-defined theories: chiral and anti-chiral whose three-point functions correspond to the two new solutions. These two theories are supposed to give a quantum complete and local example of gravitational bulk duals.