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Hidden sectors of Chern-Simons Matter theories and Exact Holography

Sachin Jain, Dhruva K. S, Evgeny Skvortsov

TL;DR

This work identifies two closed subsectors of Chern-Simons matter theories—the (anti-)chiral higher-spin sectors—by leveraging the anti-chiral and chiral limits that project boundary correlators onto purely negative or positive helicity structures. It develops a CFT3 framework using epsilon transforms and spinor-helicity variables to classify two- and three-point functions, including inside and outside the spin triangle, and demonstrates that contact terms can reconcile Ward identities and parity-odd contributions. The paper then shows that the anti-chiral limit yields a consistent, solvable subsector whose correlators are mirrored by a local bulk dual (Chiral higher-spin gravity) and discusses implications for higher-point functions, loop corrections, and anomalous dimensions, highlighting a convergent 1/$N$ expansion. These results pave the way for exact AdS4/CFT3 pairs with nontrivial, computable bulk and boundary theories and suggest extensions to SDYM/SDGR and supersymmetric Chern-Simons matter theories. Overall, the work provides a concrete, calculable route to exact holographic models with hidden chiral subsectors in three-dimensional CFTs.

Abstract

Chiral higher-spin gravity is a higher-spin extension of both self-dual Yang-Mills and self-dual gravity and is a unique local higher-spin gravity in four dimensions. Its existence implies that there are two closed subsectors in Chern-Simons matter theories. We make first steps in identifying these (anti-)chiral subsectors directly on the CFT side, which should result in a holographically dual pair where both sides are nontrivial, complete, yet exactly soluble. We also discuss closely related theories: self-dual Yang-Mills (SDYM) and self-dual gravity (SDGR) in the holographic context.

Hidden sectors of Chern-Simons Matter theories and Exact Holography

TL;DR

This work identifies two closed subsectors of Chern-Simons matter theories—the (anti-)chiral higher-spin sectors—by leveraging the anti-chiral and chiral limits that project boundary correlators onto purely negative or positive helicity structures. It develops a CFT3 framework using epsilon transforms and spinor-helicity variables to classify two- and three-point functions, including inside and outside the spin triangle, and demonstrates that contact terms can reconcile Ward identities and parity-odd contributions. The paper then shows that the anti-chiral limit yields a consistent, solvable subsector whose correlators are mirrored by a local bulk dual (Chiral higher-spin gravity) and discusses implications for higher-point functions, loop corrections, and anomalous dimensions, highlighting a convergent 1/ expansion. These results pave the way for exact AdS4/CFT3 pairs with nontrivial, computable bulk and boundary theories and suggest extensions to SDYM/SDGR and supersymmetric Chern-Simons matter theories. Overall, the work provides a concrete, calculable route to exact holographic models with hidden chiral subsectors in three-dimensional CFTs.

Abstract

Chiral higher-spin gravity is a higher-spin extension of both self-dual Yang-Mills and self-dual gravity and is a unique local higher-spin gravity in four dimensions. Its existence implies that there are two closed subsectors in Chern-Simons matter theories. We make first steps in identifying these (anti-)chiral subsectors directly on the CFT side, which should result in a holographically dual pair where both sides are nontrivial, complete, yet exactly soluble. We also discuss closely related theories: self-dual Yang-Mills (SDYM) and self-dual gravity (SDGR) in the holographic context.
Paper Structure (29 sections, 151 equations, 1 figure, 1 table)

This paper contains 29 sections, 151 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Outline:
  3. Some generalities about correlators in $\text{CFT}_3$
  4. Two-point functions
  5. Three-point functions
  6. Three-point functions inside the triangle
  7. Three-point functions that are outside the triangle
  8. Quasi-Fermionic Theory
  9. (Anti-)chiral limit for Chern-Simons matter theory
  10. Two-point functions
  11. Three-point functions
  12. Beyond three-point
  13. Four-point functions
  14. Anomalous dimensions in the (anti-)chiral limit
  15. Holographic predictions for correlators
  16. ...and 14 more sections

Figures (1)

  • Figure 1: Chern-Simons vector models vs. higher-spin gravity: the structure of AdS/CFT duality. The spectrum of fields/operators is the same (free theory in the bulk/$2$-point correlators on the boundary). (Anti)-chiral sectors together cover all cubic vertices/three-point functions. There are non-chiral parts at higher orders.