Chiral Higher-Spin Gravity Overview

• Chiral higher-spin gravity is a higher-spin theory defined by its one-sided (chiral) cubic vertices in 4D, incorporating all massless spins including the scalar and graviton.
• It uses a light-cone formulation with cubic interactions fixed by helicity algebra and admits covariant formulations via free differential algebras and homotopy techniques to ensure locality.
• The framework extends to lower dimensions with variations such as asymmetric AdS3 Chern–Simons models and topologically massive theories, offering insights into holography and UV finiteness.

Chiral higher-spin gravity denotes a class of higher-spin theories in which only one chiral sector of interaction vertices is retained. In the standard four-dimensional usage, it refers to the light-cone theory of massless fields of all spins, including the scalar and graviton, whose cubic couplings are fixed by helicity data and kept only for one sign of total helicity; the same theory admits covariant formulations as a free differential algebra and as a homotopy-algebraic minimal model in flat space and in $(A)dS_4$ (Skvortsov et al., 2022, Sharapov et al., 2022). The expression is also used in distinct lower-dimensional settings, including asymmetric $AdS_3$ Chern–Simons boundary conditions, topologically massive higher-spin theories at a chiral point, and a recent non-relativistic three-dimensional massive theory obtained from a Lifshitz deformation and null reduction of chiral massless higher-spin gravity in $AdS_4$ (Krishnan et al., 2017, Bagchi et al., 2011, Mitra et al., 25 Nov 2025).

1. Defining features of the four-dimensional theory

The four-dimensional theory is presented as a unique class of local higher-spin gravities with propagating massless fields. In the light-cone description, the spectrum contains all integer spins starting from the scalar, together with the graviton, and each massless spin-$s$ field is represented by helicity components $\Phi^{\pm s}$ or, in the covariant spinorial language, by gauge-potential-like and curvature-like chiral fields. The theory is called chiral because its interaction vertices are helicity-asymmetric: only one chiral half of the admissible cubic structures is kept, while the opposite-helicity sector is absent (Skvortsov et al., 2018, Guarini, 6 Mar 2026).

This four-dimensional chiral theory is repeatedly related to self-dual Yang–Mills and self-dual gravity. These appear as closed subsectors or consistent truncations, and the full chiral higher-spin theory extends their self-dual logic to an infinite higher-spin tower (Jain et al., 2024, Dongen, 27 Dec 2025). Several papers also treat chiral HiSGRA as the smallest or minimal higher-spin extension of gravity in the sense that nontrivial consistency requires an infinite tower, while the light-cone interaction structure remains exceptionally economical (Skvortsov et al., 2020, Sharapov et al., 2022).

The adjective “chiral” does not mean parity invariance; rather, the explicit coupling pattern discriminates between helicities, and one paper states directly that the theory violates parity (Skvortsov et al., 2020). In the same literature, locality is a central claim: chiral HiSGRA is singled out as a local interacting higher-spin theory in four dimensions, both in flat space and after smooth deformation to $(A)dS_4$ (Sharapov et al., 2022, Sharapov et al., 2022).

2. Light-cone construction and cubic interaction data

The original construction is light-front based. In flat space and in $AdS_4$, the nontrivial information resides in the dynamical generators, while the cubic vertices are fixed by closure of the relevant symmetry algebra. In the four-dimensional flat-space formulation, the universal three-point kinematics is encoded by

$$V_{\lambda_1,\lambda_2,\lambda_3}\sim [12]^{\lambda_1+\lambda_2-\lambda_3}[23]^{\lambda_2+\lambda_3-\lambda_1}[13]^{\lambda_1+\lambda_3-\lambda_2},$$

with couplings fixed as

$$C_{\lambda_1,\lambda_2,\lambda_3} = \kappa\,(l_p)^{\lambda_1+\lambda_2+\lambda_3-1}\Gamma(\lambda_1+\lambda_2+\lambda_3)^{-1}.$$

The chiral branch keeps precisely the vertices with positive total helicity, $\lambda_1+\lambda_2+\lambda_3>0$ (Guarini, 6 Mar 2026).

In the $AdS_3$0 light-cone theory discussed by Metsaev, Skvortsov, and Tran, each massless spin-$AdS_3$1 field is represented by two helicity components $AdS_3$2, and chirality means that at cubic order only one type of vertices survives, holomorphic or anti-holomorphic. The non-relativistic construction of (Mitra et al., 25 Nov 2025) quotes the holomorphic choice explicitly and gives the corresponding cubic vertex in terms of the Metsaev polynomial. The same source emphasizes that the relevant light-front formalism separates kinematical generators from dynamical generators $AdS_3$3, with the latter fixing interactions (Mitra et al., 25 Nov 2025).

A recurring source of confusion is the relation between the cubic light-cone action and the covariant theory. In the light-cone formulation, the interaction truncates at cubic order; by contrast, the covariant FDA or minimal-model description generally contains infinitely many higher local vertices. This is not presented as a contradiction but as a consequence of covariantization and of transferring the theory from light-cone variables to a manifestly Lorentz-covariant homotopy-algebraic framework (Sharapov et al., 2022, Skvortsov et al., 2022).

3. Covariant free differential algebras, minimal models, and homotopy algebra

A major development was the covariant reformulation of chiral HiSGRA as a free differential algebra,

$AdS_3$4

with $AdS_3$5 a one-form sector and $AdS_3$6 a zero-form sector. The papers on the minimal model identify this FDA with the minimal model, in the sense of $AdS_3$7-algebras, of the jet-space BV-BRST complex of chiral HiSGRA. In that formulation, the nilpotency condition $AdS_3$8 packages equations of motion, gauge identities, higher consistency conditions, counterterms, anomalies, and related cohomological data (Sharapov et al., 2022, Skvortsov et al., 2022).

The algebraic structure is not the standard twisted-adjoint one familiar from Vasiliev theory. Instead, the covariant construction uses a dual or coadjoint module for the zero-form sector, together with a higher-spin algebra realized by a Moyal–Weyl-type star product. This dual-module choice is explicitly identified as one of the ingredients responsible for the smooth flat limit and for the locality properties of the resulting vertices (Sharapov et al., 2022, Dongen, 27 Dec 2025). In the later amplitude analysis, the covariant fields are written as $AdS_3$9 and $AdS_4$0, separating the two helicities into independent chiral variables (Guarini, 6 Mar 2026).

The all-order interaction maps were then made explicit by homological perturbation theory. Several papers show that the relevant $AdS_4$1-algebra is of pre-Calabi–Yau type, and that its multilinear products can be written as integrals over compact configuration spaces of convex or concave polygons. The corresponding $AdS_4$2-relations are proved by a Stokes-theorem argument in direct analogy with formality constructions of Kontsevich, Shoikhet, and Tsygan (Sharapov et al., 2022, Sharapov et al., 2023). This suggests a close structural relation between chiral HiSGRA and noncommutative deformation quantization.

A parallel covariantization is twistorial. The twistor-action approach constructs a holomorphic Chern–Simons theory on twistor space that reproduces all known cubic chiral higher-spin vertices in flat space and yields a spacetime action there. In that description, the infinity twistor controls the cosmological constant, the star product generates the derivative structure, and the flat limit reproduces the light-cone three-point amplitudes associated with Bengtsson and Metsaev (Tran, 2022).

4. Amplitudes, ultraviolet behavior, and exact solutions

The amplitude sector is one of the most distinctive features of chiral HiSGRA. In the flat-space light-cone model, all physical tree amplitudes vanish on shell. The 2018 quantum analysis describes this as a “coupling conspiracy”: the theory has nontrivial local cubic interactions, but the contributions of the infinite tower cancel so that the full perturbative quantum $AdS_4$3-matrix is trivial, $AdS_4$4 (Skvortsov et al., 2018). Later amplitude work in the covariant formulation recovers the same cubic amplitudes from the FDA equations and, for a higher-spin extension of self-dual Yang–Mills obtained as a truncation, solves Berends–Giele recursion relations and again confirms that all tree-level amplitudes vanish (Guarini, 6 Mar 2026).

The loop sector is treated with similar emphasis. One paper shows that chiral higher-spin gravity is one-loop finite: all one-loop $AdS_4$5-matrix elements are UV-convergent, and for any number of legs they coincide with all-plus helicity one-loop amplitudes in pure QCD and SDYM, modulo a higher-spin dressing (Skvortsov et al., 2020). The earlier quantum analysis argues that the relevant spin sum regularizes to

$AdS_4$6

so one-loop vacuum and legged diagrams vanish, and the full perturbative quantum $AdS_4$7-matrix remains $AdS_4$8 (Skvortsov et al., 2018). A companion study strengthens this picture for two-, three-, and four-point amplitudes at one loop and also discusses Yang–Mills gaugings with $AdS_4$9, $s$0, and $s$1 groups, in direct analogy with Chan–Paton structure (Skvortsov et al., 2020).

The exact-solution sector exhibits a different manifestation of chirality. At $s$2, chiral higher-spin gravity admits exact self-dual pp-wave solutions constructed from harmonic scalar functions and principal spinors. These configurations satisfy both the linear and nonlinear equations because the chosen ansatz annihilates the higher-order vertices: the spin-2 field generates a self-dual pp-wave background, and the higher-spin fields propagate freely on that background (Tran, 11 Jan 2025). This suggests that special self-dual sectors of chiral HiSGRA are rigid enough for the full nonlinear interaction structure to collapse to free propagation on nontrivial backgrounds.

5. Holography, hidden subsectors, and supersymmetric extensions

The holographic interpretation is centered on Chern–Simons matter theories and vector models. The existence of a local chiral higher-spin gravity in $s$3 is presented as evidence that Chern–Simons vector models contain closed chiral and anti-chiral subsectors, with consequences for three-dimensional bosonization duality (Sharapov et al., 2022, Sharapov et al., 2022). A later study develops this into an “exact holography” program: momentum-space correlators in three-dimensional spinor-helicity variables are used to isolate chiral subsectors directly on the CFT side, and the chiral or anti-chiral bulk limit is described by setting one of two couplings, $s$4 or $s$5, to zero (Jain et al., 2024).

The homotopy-algebraic literature pushes the same idea further. The covariant, coordinate-independent $s$6 formulation is said to demonstrate, via AdS/CFT, that $s$7 vector models possess a closed chiral subsector organized by the same algebraic data (Dongen, 27 Dec 2025). In the same vein, the twistor-action and self-dual-solution papers repeatedly associate chirality with integrability or exact solvability, although those claims are typically formulated as expectations, conjectures, or strong indications rather than as general theorems (Tran, 2022, Tran, 11 Jan 2025).

Supersymmetric versions preserve the central light-front features. The $s$8 and $s$9 supersymmetric chiral HiSGRAs have purely cubic classical actions in superspace, admit light-front Feynman rules, and continue to exhibit vanishing on-shell tree amplitudes and vanishing one-loop amplitudes after the relevant cancellations and regularization. The same work also performs a dimensional reduction to a $\Phi^{\pm s}$0, $\Phi^{\pm s}$1 system with massive higher-spin fields arranged on a mass lattice (Tsulaia et al., 2022).

6. Lower-dimensional usages and terminological variants

Outside the standard four-dimensional massless theory, “chiral higher-spin gravity” names several distinct constructions. One important $\Phi^{\pm s}$2 usage is the Chern–Simons boundary-condition problem studied for $\Phi^{\pm s}$3. There the left sector is Drinfeld–Sokolov reduced while the right sector retains all charges and chemical potentials. For the spin-3 case this gives 19 independent functions, and the asymptotic symmetry algebra is

$\Phi^{\pm s}$4

The resulting metric fits the generalized Grumiller–Riegler notion of the most general $\Phi^{\pm s}$5 boundary conditions (Krishnan et al., 2017).

A second $\Phi^{\pm s}$6 usage appears in topologically massive higher-spin gravity. The spin-3 generalization of topologically massive gravity adds a parity-violating Chern–Simons-like term to the Fronsdal action, producing propagating massive bulk modes in three dimensions. Its chiral point is the familiar

$\Phi^{\pm s}$7

where the massive and left-moving branches degenerate and logarithmic modes appear. Unlike the spin-2 case, there is a nontrivial trace sector together with a trace logarithmic partner; the logarithmic partner of the traceless mode carries negative energy, indicating an instability at the chiral point (Bagchi et al., 2011).

A third and conceptually different construction is the non-relativistic chiral massive higher-spin gravity of (Mitra et al., 25 Nov 2025). Starting from the standard light-cone chiral higher-spin theory of Metsaev, Skvortsov, and Tran in $\Phi^{\pm s}$8, the authors apply a Lifshitz deformation and then a null reduction. The result is a three-dimensional, massive, non-relativistic theory in a deformed $\Phi^{\pm s}$9 geometry. It remains chiral in the sense that the one-sided cubic interaction sector is inherited from the parent four-dimensional theory, but the resulting vertices are less constrained because the reduced non-relativistic symmetry algebra does not provide enough dynamical generators to fix the couplings uniquely. The same paper proposes an approximate mass-spin relation interpolating between relativistic and non-relativistic regimes, argues that higher-spin interactions become suppressed at large spin, states explicitly that the resulting $(A)dS_4$0 gravity is not topological, and conjectures a two-dimensional non-relativistic Landau–Ginzburg dual describing a two-fluid system with a $(A)dS_4$1-point constraint in one spatial dimension (Mitra et al., 25 Nov 2025).

These lower-dimensional examples are related to the four-dimensional theory by shared asymmetry of sectors, helicities, or boundary algebras, but they are not dynamically equivalent. This suggests that the phrase “chiral higher-spin gravity” tracks a family resemblance centered on one-sided interaction structures rather than a single universal model.