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

We review the theory of higher-spin gauge fields in four and three space-time dimensions and present some new results on higher-spin gauge interactions of matter fields in two dimensions.

Massive bosonic fields of arbitrary spin are predicted by general extensions of the Standard Model. It has been recently shown that there exists a family of bimetric theories of gravity - including massive gravity - which are free of Boulware-Deser ghosts at the nonlinear level. This opens up the possibility to describe consistently the dynamics of massive spin-2 particles in a gravitational field. Within this context, we develop the study of massive spin-2 fluctuations - inc...

We provide evidence that the classical scattering of two spinning black holes is controlled by the soft expansion of exchanged gravitons. We show how an exponentiation of Cachazo-Strominger soft factors, acting on massive higher-spin amplitudes, can be used to find spin contributions to the aligned-spin scattering angle, conjecturally extending previously known results to higher orders in spin at one-loop order. The extraction of the classical limit is accomplished via the on...

From the S-matrix of spinning particles, we extract the 2 PM conservative potential for binary spinning black holes up to quartic order in spin operators. An important ingredient is the exponentiated gravitational Compton amplitude in the classical spin-limit for all graviton helicity sectors. The validity of the resulting Hamiltonian is verified by matching to known lower spin order results, as well as direct computation of the 2PM impulse and spin kicks from the eikonal pha...

We review recent progress in the construction of black holes in three dimensional higher spin gravity theories. Starting from spin-3 gravity and working our way toward the theory of an infinite tower of higher spins coupled to matter, we show how to harness higher spin gauge invariance to consistently generalize familiar notions of black holes. We review the construction of black holes with conserved higher spin charges and the computation of their partition functions to lead...

Long ago, Newman and Janis showed that a complex deformation $z\rightarrow z+i a$ of the Schwarzschild solution produces the Kerr solution. The underlying explanation for this relationship has remained obscure. The complex deformation has an electromagnetic counterpart: by shifting the Coloumb potential, we obtain the EM field of a certain rotating charge distribution which we term $\sqrt{\rm Kerr}$. In this note, we identify the origin of this shift as arising from the expon...

Using the light-cone formulation of relativistic dynamics, we develop various methods for constructing cubic interaction vertices and apply these methods to the study of higher spin fields propagating in flat space of dimension greater than or equal to four. Generating functions of parity invariant cubic interaction vertices for massive and massless higher spin fields of arbitrary symmetry are obtained. We derive restrictions on the allowed values of spins and the number of d...

We review some relevant results in the context of higher spin black holes in three-dimensional spacetimes, focusing on their asymptotic behaviour and thermodynamic properties. For simplicity, we mainly discuss the case of gravity nonminimally coupled to spin-3 fields, being nonperturbatively described by a Chern-Simons theory of two independent sl(3,R) gauge fields. Since the analysis is particularly transparent in the Hamiltonian formalism, we provide a concise discussion of...

We put forward a broader picture of the effective theory of a spinning particle within the EFT of spinning gravitating objects, through which we derive and establish the new precision frontier at the fifth PN (5PN) order. This frontier includes higher-spin sectors, quadratic and quartic in the spin, which both display novel physical features, due to the extension of the effective theory beyond linear order in the curvature. The quadratic-in-spin sectors give rise to a new tid...

This is a collection of my lecture notes on the higher-spin theory course given for students at the Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University. The goal of these lectures is to give an introduction to higher-spin theories accessible to master level students which would enable them to read the higher-spin literature. I start by introducing basic relevant notions of representation theory and the associated field-theoretic descriptions....