Higher Spin Theories Research Articles

Higher-spin Yang–Mills, amplitudes and self-duality

The existence of interacting higher-spin theories is tightly constrained by many no-go theorems. In this paper, we construct a chiral, higher-spin generalization of Yang–Mills theory in flat space which avoids these no-go theorems and has non-trivial tree-level scattering amplitudes with some higher-spin external legs. The fields and action are complex, so the theory is non-unitary and parity-violating, yet we find surprisingly compact formulae for all-multiplicity tree-level scattering amplitudes in the maximal helicity violating (MHV) sector, where the two negative helicity particles have identical but arbitrary spin. This is possible because the theory admits a perturbative expansion around its self-dual sector. Using twistor theory, we prove the classical integrability of this self-dual sector and show that it can be described on spacetime by an infinite tower of interacting massless scalar fields. We also give a twistor construction of the full theory and use it to derive the formula for the MHV amplitude.

Geometric tool kit for higher-spin gravity (Part I): An introduction to the geometry of differential operators

This paper provides an introduction to the algebra and geometry of differential operators and jet bundles. Its point of view is guided by the leitmotiv that higher-spin gravity theories call for higher-order generalizations of Lie derivatives and diffeomorphisms. Nevertheless, the material covered here may be of general interest to anyone working on topics where geometrical (coordinate-free, global, generic) and mathematically rigorous definitions of differential operators are required.

Nonrelativistic spin-3 symmetries in 2+1 dimensions from expanded and extended Nappi-Witten algebras

We show that infinite families of Galilean spin-3 symmetries in $2+1$ dimensions, which include higher-spin extensions of the Bargmann, Newton-Hooke, nonrelativistic Maxwell, and nonrelativistic AdS-Lorentz algebras, can be obtained as Lie algebra expansions of two different spin-3 extensions of the Nappi-Witten symmetry. These higher-spin Nappi-Witten algebras, in turn, are obtained by means of In\"on\"u-Wigner contractions applied to suitable direct product extensions of $\mathfrak{s}\mathfrak{l}(3,\mathbb{R})$. Conversely, we show that the same result can be obtained by considering contractions of expanded $\mathfrak{s}\mathfrak{l}(3,\mathbb{R})$ algebras. The method can be used to define nonrelativistic higher-spin Chern-Simon gravity theories in $2+1$ dimensions in a systematic way.

From Moyal deformations to chiral higher-spin theories and to celestial algebras

We study the connection of Moyal deformations of self-dual gravity and self-dual Yang-Mills theory to chiral higher-spin theories, and also to deformations of operator algebras in celestial holography. The relation to Moyal deformations illuminates various aspects of the structure of chiral higher-spin theories. For instance, the appearance of the self-dual kinematic algebra in all the theories considered here leads via the double copy to vanishing tree-level scattering amplitudes. Regarding celestial holography, the Moyal deformation of self-dual gravity was recently shown to lead to the loop algebra of W∧, and we obtain here the analogous deformation of a Kac-Moody algebra corresponding to Moyal-deformed self-dual Yang-Mills theory. We also introduce the celestial algebras for various chiral higher-spin theories.

Mathcal{N} = 2 higher spins: superfield equations of motion, the hypermultiplet supercurrents, and the component structure

As a continuation of our previous papers arXiv:2109.07639 and arXiv:2202.08196, we study the linearized structure of the manifestly 4D, mathcal{N} = 2 supersymmetric theory of the cubic couplings of the higher spin gauge superfields to the matter hypermultiplets. We consider in detail the superfield equations of motion, construct the conserved hypermultiplet superfield currents, explore their component structure (basically in the bosonic sector) and compare it with the corresponding currents in the conventional higher-spin bosonic theory. We thoroughly study the mathcal{N} = 2 spin 2 and 3 models as instructive examples.

Induced action for superconformal higher-spin multiplets using SCFT techniques

Recently, the interacting N=1 superconformal higher-spin theory in four dimensions has been proposed within the induced action approach. In this paper we initiate a program of computing perturbative corrections to the corresponding action and explicitly evaluate all quadratic terms. This is achieved by employing standard techniques from superconformal field theory.

Toward a twistor action for chiral higher-spin gravity

A covariant twistor action for chiral higher-spin theory in (A)dS and flat space is constructed in terms of a holomorphic Chern-Simons theory on twistor space. The action reproduces all known cubic vertices of chiral higher-spin theory in flat space. The spacetime action of the holomorphic Chern-Simons theory in flat space is also obtained.

Late-time correlation functions in dS3/CFT2 correspondence

We compute the late-time correlation functions on three-dimensional de Sitter spacetime for a higher-spin gravity theory. For this, we elaborate on the formulation to obtain the wave functional of universe from a dual conformal field theory, which is used to compute the late-time correlation functions. We argue that the relation to direct bulk Feynman diagram computations in the in-in formulation. We furthermore provide a precise prescription to construct a higher-spin dS3 holography as an analytic continuation of Gaberdiel-Gopakumar duality for AdS3. Part of results here were already reported in an earlier letter. We explain the details of their derivations and extend the analysis to more generic cases in this paper. Previously, we have examined two- and three-point functions and a simple four-point correlator at the leading order in Newton constant. Here we also evaluate more complicated four-point correlators. Finally, we study late-time correlators in an alternative limit of dS3/CFT2 with critical level coset, such as, two-point correlator on conical defect geometry. We also examine one-loop corrections to two-point correlator on dS3.

Constraining higher-spin S-matrices

There are various no-go theorems that tightly constrain the existence of local higher-spin theories with non-trivial S-matrix in flat space. Due to the existence of higher-spin Yang-Mills theory with non-trivial scattering amplitudes, it makes sense to revisit Weinberg’s soft theorem — a direct consequence of the Lorentz invariance of the S-matrix that does not take advantage of unitarity and parity invariance. By working with the chiral representation — a representation originated from twistor theory, we show that Weinberg’s soft theorem can be evaded and non-trivial higher-spin S-matrix is possible. In particular, we show that Weinberg’s soft theorem is more closely related to the number of derivatives in the interactions rather than spins. We also observe that all constraints imposed by gauge invariance of the S-matrix are accompanied by polynomials in the soft momentum of the emitted particle where the zeroth order in the soft momentum is a charge conservation law.

Disentanglement of topological and dynamical fields in 3d higher-spin theory within shifted homotopy approach

The first-order correction to the one-form sector of equations of the 3d higher-spin theory is derived from the generating nonlinear HS system by virtue of the shifted homotopy approach. The family of solutions to the generating system that disentangles equations for dynamical and topological fields in the first order of perturbation theory is found. This family is shown to belong to the different cohomology class compared to the solution found earlier by the direct methods. The related cohomology is shown to be the same as that underlying the mass deformation in the matter sector of 3d higher-spin equations.

Instantons in AdS$$_4$$ from (anti)membranes wrapping $$S^7$$ to Bose–Fermi duality in CFT$$_3$$’s

We present new SO(4)-invariant and non-supersymmetric instanton solutions for the conformally coupled m^2=-2 and massive m^2=+4 (pseudo)scalars arising from a consistent truncation of 11-dimensional supergravity over AdS_4 x S^7/Z_k when the internal space is a S^1 Hopf fibration on CP^3, and we consider backreaction. In fact, the bulk configurations associate with (anti)membranes wrapped around mixed internal (and external) directions, which in turn probe the Wick-rotated or skew-whiffed background, break all supersymmetries as well as parity invariance. From near the boundary behavior of the closed solution for the coupled bulk (pseudo)scalar, we get a marginal triple-trace deformation with mixed boundary condition (valid also for the bulk massless m^2=0 (pseudo)scalar, raised when considering the external space backreaction, with Dirichlet boundary condition) and as a result, the corresponding boundary effective potential is unbounded from below and causes an instability because of the Fubini-like instanton. Presenting dual effective actions, we see that the boundary solutions and counterparts realize in singlet sectors of three-dimensional U(N) and O(N) Chern--Simons-matter field theories. In particular, we use versions of massless and mass-deformed regular and critical boson and fermion models, find instantons and confirm state-operator AdS_4/CFT_3 correspondence and also Bose-Fermi duality at the level of the solutions. In addition, we discuss on relations of our setups with Vasiliev's Higher-Spin theories, deformations of the Aharony-Bergman-Jafferis-Maldacena model and other related studies.

Towards higher-spin holography in flat space

We study the chiral flat space higher-spin algebra, which is the global symmetry algebra of the chiral higher-spin theory in the 4d Minkowski space. We find that it can be constructed as the universal enveloping algebra of a certain chiral deformation of the Poincaré algebra quotiented by a set of quadratic identities. These identities allow us to identify a representation of the latter algebra, which by analogy with the AdS space higher-spin holography, we interpret as the flat space singleton representation. We provide two explicit realisations of this singleton representation — in terms of sl(2, ℂ) spinors and in terms of oscillator-like variables — as well as briefly discuss its properties.

Chiral higher-spin holography in flat space: the Flato-Fronsdal theorem and lower-point functions

We prove the flat space analogue of the Flato-Fronsdal theorem. It features the flat space singleton representation suggested recently. We do that by deriving a kernel that intertwines a pair of singleton representations with massless higher-spin fields in flat space. Next, we derive two-point functions of flat space singletons, which are then used to construct two- and three-point scattering amplitudes in the dual theory of massless higher-spin fields. These amplitudes agree with amplitudes in the chiral higher-spin theory.

A twistorial description of the IKKT-matrix model

We consider the fuzzy 4-sphere {S}_N^4 as a background in the IKKT matrix model, and explore the relation between {S}_N^4 and fuzzy twistor space in the semi-classical limit. A novel description for the IKKT-matrix model in terms of spinorial indices is given, which is reminiscent of mathcal{N} = 4 super-symmetric Yang-Mills (SYM) in 4d. On fuzzy twistor space, the interactions of the IKKT model are of gravitational type. The higher-spin (HS) gauge theory emerging in this limit from the IKKT model, denoted as HS-IKKT, on fuzzy twistor space is shown to be a higher-spin extension of mathcal{N} = 4 SYM, with vertices that have more than two derivatives. We obtain its (Euclidean) spacetime action using the Penrose transform. Although this is a gravitational theory, it shares many features with the higher-spin extensions of Yang-Mills in 4d flat space obtained in [1, 2]. The tree-level amplitudes of the HS-IKKT are studied in the semi-classical flat limit. The self-dual gauge sector of the IKKT model is obtained by dropping some parts of the cubic- and the quartic interactions, which is shown to reduce to a mathcal{BF} -type action on commutative deformed projective twistor space.

Massless scalars and higher-spin BMS in any dimension

Starting from the asymptotic kinematics of massless scalar fields near null infinity in any spacetime dimension, we build two higher-spin extensions of the Carrollian definition of the BMS group and its generalisations. The first extension exhibits conformal properties reminiscent of the singleton in Anti-de Sitter space. The second acts on the space of radiative solutions of the d’Alembert equation, i.e. on Sachs’s representation of BMS, which we relate to the scalar massless Poincaré representation and extend to any Carrollian manifold. The corresponding enveloping algebra is a higher-spin extension of BMS that can be interpreted as the asymptotic symmetry of a putative exotic higher-spin gravity theory around Minkowski spacetime. Along the way, we provide a pedagogical introduction to Carrollian geometry and its relation to BMS.

On holomorphic sector of higher-spin theory

Recent investigation of the locality problem for higher-spin fields led to a vertex reconstruction procedure that involved elements of contraction of the original Vasiliev interaction algebra. Inspired by these results we propose the Vasiliev-like generating equations for the holomorphic higher-spin interactions in four dimensions based on the observed contracted algebra. We specify the functional class that admits evolution on the proposed equations and brings in a systematic procedure of extracting all-order holomorphic vertices. A simple consequence of the proposed equations is the space-time locality of the gauge field sector. We also show that vertices come with a remarkable shift symmetry.

Chiral higher spin gravity in (A)dS4 and secrets of Chern–Simons matter theories

Chiral Higher Spin Gravity with cosmological constant is constructed as a Free Differential Algebra, i.e. at the level of equations of motion, which is a smooth deformation of its flat space cousin [34]. Chiral Higher Spin Gravity is a unique class of local higher spin theories; its very existence implies that there is a closed and, most likely, integrable sub-sector of Chern–Simons Matter Theories, which has important consequences both for the theories themselves and for three-dimensional bosonization duality.

Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes

We sum up two- and three-point amplitudes in the chiral higher-spin theory over helicities and find that these quite manifestly have the form of invariant traces of the flat space chiral higher-spin algebra. We consider invariant traces of products of higher numbers of on-shell higher-spin fields and interpret these as higher-point scattering amplitudes. This construction closely mimics its anti-de Sitter space counterpart, which was considered some time ago and was confirmed holographically.

Projectively-compact spinor vertices and space-time spin-locality in higher-spin theory

The concepts of compact and projectively-compact spin-local spinor vertices are introduced. Vertices of this type are shown to be space-time spin-local, i.e., their restriction to any finite subset of fields is space-time local. The known spinor spin-local cubic vertices with the minimal number of space-time derivatives are verified to be projectively-compact. This has the important consequence that spinor spin-locality of the respective quartic vertices would imply their space-time spin-locality. More generally, it is argued that the proper class of solutions of the non-linear higher-spin equations that leads to the minimally non-local (presumably space-time spin-local) vertices is represented by the projectively-compact vertices. The related aspects of the higher-spin holographic correspondence are briefly discussed.

Disordered Vector Models: From Higher Spins to Incipient Strings.

We present a one-parameter family of large N disordered models, with and without supersymmetry, in three spacetime dimensions. They interpolate from the critical large N vector model dual to a classical higher spin theory toward a theory with a classical string dual. We analyze the spectrum and operator product expansion data of the theories. While the supersymmetric model is always well-behaved the nonsupersymmetric model is unitary only over a small parameter range. We offer some speculations on the origin of strings from the higher spins.