Conformal higher-spin gravity is the log-divergent part of the effective action of the scalar field coupled to background fields via higher-spin currents, as was defined by Segal and Tseytlin, which can be worked out over the flat space background. We revisit the problem of the scalar field in a higher-spin background and propose a manifestly covariant version thereof. The construction utilizes the Fedosov quantization of the cotangent bundle and the action is written with the help of the trace on a curved phase space that is provided by the Feigin-Felder-Shoikhet cocycle. The same construction allows one to formulate quantum mechanics on a curved space, the phase space being the cotangent bundle.

Belgium

Thomas Basile

Shailesh Dhasmana

Evgeny Skvortsov

Scalar field on a higher-spin background via Fedosov quantization

<p>Nontrivial conformal field theories are rare. Motivated by the recent construction of a local higher-spin gravity in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>AdS</mi><mn>4</mn></msub></math>—chiral higher-spin gravity—we begin to identify its anti–de Sitter/conformal field theory (AdS/CFT) dual theory that has to be a closed subsector of Chern-Simons matter theories, thereby shedding more light on this class of CFTs and the dualities that relate them. We show that at the level of two- and three-point functions the sub-CFT can be defined as a limit of Chern-Simons matter theories where only correlators with the total positive (or negative) helicity are kept. We also discuss extension to higher orders and list a number of nontrivial predictions from the bulk.</p>

India

Sachin Jain

Dhruva K. S

Hidden sectors of Chern-Simons matter theories and exact holography

Massless higher-spin fields show no preference for any value of the cosmological constant in 3$\textit{d}$. All matter-free higher-spin gravities in 3d are equivalent to Chern-Simons theories with an appropriate choice of gauge algebra. For various reasons, including holography, it is important to enrich them with matter fields. In ($\textit{A}$)$\textit{dS}$ , the coupling of matter fields to higher-spin fields is well-known to the leading order and is determined by the representation theory. We extend this result to flat space, where the relevant higher-spin algebra is the Poisson algebra, aka $\textit{w}$ . However, we show that both in flat and ($\textit{A}$)$\textit{dS}$ spaces there are no nontrivial higher order deformations/interactions. Nevertheless, by enlarging the field content with some auxiliary fields and taking advantage of the chiral higher-spin gravity’s vertices, it is possible to construct an exotic matter-coupled theory on ($\textit{A}$)$\textit{dS}$ that is perturbatively local. It also admits a flat limit. The equations of motion have the form of a Poisson sigma-model and a meaningful action has the form of a Courant sigma-model. We also explore the potential for embedding this theory into a holographic duality.

Russia

Alexey Sharapov

Arseny Sukhanov

Matter-coupled higher spin gravities in 3$\textit{d}$: no- and yes-go results

We address the issue of electromagnetic interaction for massive higher-spin fields in three-dimensional Minkowski space. We show that consistent field equations can be obtained through the dimensional reduction of the higher-spin extension of self-dual Yang–Mills theory, which itself is a truncation of chiral higher-spin gravity in four dimensions. The resulting electromagnetic field satisfies the Bogomolny equation, and the interaction is non-minimal with the gyromagnetic ratio given by $$g=1/s$$ , where is the spin. As a by-product, we obtain a new Lagrangian for free massive higher-spin fields in 3 .

David Shcherbatov

Electromagnetic interactions of massive higher-spin fields in 3D via chiral theory

We develop massive higher-spin theory as a framework for describing dynamics of rotating compact objects, such as Kerr black holes. In this paper, we explore gauge interactions up to quartic order and corresponding Compton amplitudes of higher-spin massive objects coupled to electromagnetism and Yang-Mills theory. Their classical counterparts are known as root-Kerr gauge-theory solutions, whose amplitudes are closely related to those of Kerr black holes. We use three distinct approaches: (i) massive higher-spin gauge symmetry to introduce cubic interactions for all spins and the quartic interactions up to spin 3, which is implemented both off shell and via Ward identities; (ii) a chiral higher-spin approach to construct quartic Lagrangians with correct degrees of freedom to all spins; (iii) on-shell functional patterns before and after taking the classical limit to constrain the Compton amplitudes. As final results, we arrive at simple local formulae for the candidate root-Kerr Compton amplitudes both in the quantum regime and classical limit, to all orders in spin. This is a precursor to the gravitational Kerr case, which is presented in a follow-up paper.

Sweden

Lucile Cangemi

Marco Chiodaroli

Henrik Johansson

United Kingdom

China

Alexander Ochirov

Paolo Pichini

From higher-spin gauge interactions to Compton amplitudes for root-Kerr

Massive higher-spin fields are difficult to introduce consistent interactions, including electromagnetic and gravitational ones which are clearly exhibited by (non-elementary) higher-spin particles in nature. We construct an action that describes consistent interactions of massive spin three-half field with a constant electromagnetic background. We also work out the relation to the chiral approach.

William Delplanque

Massive spin three-half field in a constant electromagnetic background

We construct a candidate tree-level gravitational Compton amplitude for a rotating Kerr black hole, for any quantum spin <math><mrow><mi>s</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>∞</mi></mrow></math>, from which we extract the corresponding classical amplitude to all orders in the spin vector <math><msup><mi>S</mi><mi>μ</mi></msup></math>. We use multiple insights from massive higher-spin quantum field theory, such as massive gauge invariance and improved behavior in the massless limit. A chiral-field approach is particularly helpful in ensuring correct degrees of freedom, and for writing down compact off-shell interactions for general spin. The simplicity of the interactions is echoed in the structure of the spin-<math><mi>s</mi></math> Compton amplitude, for which we use homogeneous symmetric polynomials of the spin variables. Where possible, we compare to the general-relativity results in the literature, available up to eighth order in spin.

Compton Amplitude for Rotating Black Hole from QFT

Higher spin gravities do not have a low energy limit where higher-spin fields decouple from gravity. Nevertheless, it is possible to construct fine-tuned exact solutions that activate low-spin fields without sourcing the higher-spin fields. We show that BPST (Belavin-Polyakov-Schwartz-Tyupkin) instanton is an exact solution of Chiral Higher Spin Gravity, i.e. it is also a solution of the holographic dual of Chern-Simons matter theories. This gives an example of a low-spin solution. The instanton sources the opposite helicity spin-one field and a scalar field. We derive an Effective Field Theory that describes the coupling between an instanton and the other two fields, whose action starts with the Chalmers-Siegel action and has certain higher derivative couplings.

Yihao Yin

Low spin solutions of higher spin gravity: BPST instanton

Chiral higher spin gravity is defined in terms of a strong homotopy algebra of pre-Calabi-Yau type (noncommutative Poisson structure). All structure maps are given by the integrals over the configuration space of concave polygons and the first two maps are related to the (Shoikhet-Tsygan-)Kontsevich Formality. As with the known formality theorems, we prove the A  ∞ -relations via Stokes’ theorem by constructing a closed form and a configuration space whose boundary components lead to the A  ∞ -relations. This gives a new way to formulate higher spin gravities and hints at a construct encompassing the known formality theorems.

Richard Dongen

Strong homotopy algebras for chiral higher spin gravity via Stokes theorem

Motivated by the generation of action principles from off-shell dualisation, we present a general class of free, topological theories in three dimensional Minkowski spacetime that exhibit higher-spin gauge invariance. In the spin-two case, we recover a dual reformulation of the triplet system already known, while the higher-spin systems that we obtain seem to be new. They are associated with wild quivers. We study in which situations these exotic (or strange) higher-spin models can be extended to dS and AdS backgrounds, revealing that the flat limit of such models, when they exist, admits a one-parameter freedom. Interactions are studied in the simplest higher-spin case featuring spin-2 and spin-3 fields. We then give several higher-spin generalizations of these strange systems.