A chiral limit for Chern-Simons-matter theories

TL;DR

This paper explores the relationship between correlation functions in large N quasi-fermionic Chern-Simons-matter theories and a specific form of higher-spin gravity vertices, revealing a chiral limit where the dual theory simplifies.

Contribution

It demonstrates that all relations between 3-point structures in these theories follow from a particular form of higher-spin gravity vertices, connecting field theory and gravity in a new way.

Findings

Relations between 3-point structures follow from Skvortsov's vertices.

A specific limit simplifies the dual higher-spin gravity to a chiral theory.

Analytic continuation to complex couplings relates to a chiral limit in the dual theories.

Abstract

Large N quasi-fermionic Chern-Simons-matter theories have an approximate higher-spin symmetry that strongly constrains their correlation functions. In particular, the 3-point functions for generic spins are combinations of 3 structures (with specific dependence on the positions and helicities), and the coupling-dependence of the coefficient of each structure is uniquely determined. In the past few years, several relations between different structures were found. In this paper we show that all the relations between the structures follow from (or, conversely, they imply) a specific form written by Skvortsov for the vertices of the dual higher-spin gravity theory on four-dimensional anti-de Sitter space, when written in spinor-helicity variables. The dual bulk theory has a specific limit where it simplifies and becomes a "chiral higher-spin gravity theory", and we discuss what can be said about this limit in the dual Chern-Simons-matter theories, where it involves an analytic continuation to complex couplings.