We use a recently proposed covariant procedure to reduce the Chern-Simons action of three-dimensional higher-spin gravity to the boundary, resulting in a Lorentz covariant action for higher-order chiral scalars. After gauge-fixing, we obtain a higher-derivative action generalizing the $\textit{s}$ = 1 Floreanini-Jackiw and $\textit{s}$ = 2 Alekseev-Shatashvili actions to arbitrary spin s. For simplicity, we treat the case of general spin at the linearized level, while the full non-linear asymptotic boundary conditions are presented in component form for the SL(3, ℝ) case. Finally, we extend the spin-3 linearized analysis to a background with non-trivial higher-spin charge and show that it has a richer structure of zero modes.

United Kingdom

Taiwan

Calvin Chen

South Korea

Euihun Joung

Karapet Mkrtchyan

Junggi Yoon

Higher-order chiral scalar from boundary reduction of 3d higher-spin gravity

All independent interaction vertices involving massless (Fang-Fronsdal) fermions in three dimensions are classified, completing the classification of interactions of massless fields of any spin. Similar to the bosonic case, we get no independent vertices at quartic or higher order in the fields involving fields with spin <math><mi>s</mi><mo>≥</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> and cubic vertices only for spins satisfying triangle inequalities, apart from the cases involving (matter) fields with spin <math><mi>s</mi><mo>≤</mo><mn>1</mn></math>. Different from the bosonic cases, we get only one vertex for each triple of spins with two Majorana fermions and one boson, which is parity even (odd) when the sum of the spins of all fields involved is odd (even). When the two Majorana fermions are identical, their coupling to an odd-spin boson is trivialized. We comment on the nontrivial holographic dictionary relating these vertices to conformal field theory correlators in two dimensions.

Austria

Stefan Fredenhagen

Filipp Lausch

Germany

Interactions of massless fermionic fields in three dimensions

The spinor-helicity representations of massive and (partially) massless particles in four-dimensional (anti–)de Sitter (A)dS spacetime are studied within the framework of the dual pair correspondence. We show that the dual groups (also known as “little groups”) of the anti–de Sitter and de Sitter groups are, respectively, <math><mrow><mi>O</mi><mo>(</mo><mn>2</mn><mi>N</mi><mo>)</mo></mrow></math> and <math><mrow><msup><mrow><mi>O</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>(</mo><mn>2</mn><mi>N</mi><mo>)</mo></mrow></math>. For <math><mi>N</mi><mo>=</mo><mn>1</mn></math>, the generator of the dual algebra <math><mrow><mi>so</mi><mo>(</mo><mn>2</mn><mo>)</mo><mo>≅</mo><msup><mrow><mi>so</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>(</mo><mn>2</mn><mo>)</mo><mo>≅</mo><mi>u</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math> corresponds to the helicity operator, and the spinor-helicity representation describes massless particles in (A)<math><msub><mtext>dS</mtext><mn>4</mn></msub></math>. For <math><mi>N</mi><mo>=</mo><mn>2</mn></math>, the dual algebra is composed of two ideals, <math><mi>s</mi></math> and <math><msub><mi>m</mi><mi>Λ</mi></msub></math>. The former ideal <math><mi>s</mi><mo>≅</mo><mi>so</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> fixes the spin of the particle, while the mass is determined by the latter ideal <math><msub><mi>m</mi><mi>Λ</mi></msub></math>, which is isomorphic to <math><mi>so</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math>, <math><mi>iso</mi><mo>(</mo><mn>2</mn><mo>)</mo></math>, or <math><mi>so</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> depending on the cosmological constant being positive, zero, or negative. In the case of a positive cosmological constant, namely <math><mrow><msub><mrow><mi>dS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math>, the spinor-helicity representation contains all massive particles corresponding to the principal series representations and the partially massless particles corresponding to the discrete series representations leaving out only the light massive particles corresponding to the complementary series representations. The zero and negative cosmological constant cases, which had been addressed in earlier references, are also discussed briefly. Finally, we consider the multilinear form of helicity spinors invariant under (A)dS group, which can serve as the (A)dS counterpart of the scattering amplitude, and discuss technical differences and difficulties of the (A)dS cases compared to the flat spacetime case.

Belgium

Thomas Basile

Matin Mojaza

Spinor-helicity representations of particles of any mass in <math><mrow><msub><mrow><mi>dS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> and <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> spacetimes

We revisit the problem of classification and explicit construction of the conformal three-point correlation functions of currents of arbitrary integer spin in arbitrary dimensions. For the conserved currents, we set up the equations for the conservation conditions and solve them completely for some values of spins, confirming the earlier counting of the number of independent structures matching them with the higher-spin cubic vertices in one higher dimension. The general solution for the correlators of conserved currents we delegate to a follow-up work.

Armenia

Melik Karapetyan

Ruben Manvelyan

On correlation functions of higher-spin currents in arbitrary dimensions d &gt; 3

Chiral form fields in <math><mi>d</mi></math> dimensions can be effectively described as edge modes of topological Chern-Simons theories in <math><mi>d</mi><mo>+</mo><mn>1</mn></math> dimensions. At the same time, manifestly Lorentz-invariant Lagrangian description of such fields directly in terms of a <math><mi>d</mi></math>-dimensional field theory is challenging and requires introducing nontrivial auxiliary gauge fields eliminated on shell with extra gauge symmetries. A recent work by Arvanitakis et al. demonstrates (emphasizing the case of 2d chiral bosons) that the two approaches are related, and a peculiar reduction on the (<math><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></math>)-dimensional topological Lagrangian automatically leads to <math><mi>d</mi></math>-dimensional Lagrangians with appropriate sets of auxiliary fields. We develop this setup in three distinct directions. First, we demonstrate how arbitrary Abelian self-interactions for chiral forms can be included using nonlinear boundary terms in the Chern-Simons theory. Second, by generalizing the Chern-Simons theory to the BF-theory, we obtain an analogous democratic description of nonchiral form fields, where electric and magnetic potentials appear as explicit dynamical variables. Third, we discuss the effects of introducing topological interactions in the higher-dimensional bulk, which produce extra interaction terms in the boundary theory. When applied to a topological 4-form field in 12 dimensions, this construction results in a democratic description of the 3-form gauge field of the eleven-dimensional supergravity.

Oleg Evnin

Democratic Lagrangians from topological bulk

We present a universal democratic Lagrangian for the bosonic sector of ten-dimensional type II supergravities, treating “electric” and “magnetic” potentials of all Ramond-Ramond (RR) fields on equal footing. For type IIB, this includes the five-form whose self-duality equation is derived from the Lagrangian. We also present an alternative form of the action for type IIB, with manifest <math><mrow><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo></mrow></math> symmetry.

Fridrich Valach

Democratic actions for type II supergravities

We study solutions in non-linear electrodynamics (NED) and establish several general results. We show, that the SO(2) electric-magnetic duality symmetry is restrictive enough to allow for reconstruction of the NED Lagrangian from the spherically-symmetric electrostatic (Coulomb-like) solution — although there are infinitely many different NED theories admitting a given solution, there exists a unique SO(2) invariant one among them under a simple analyticity assumption (that leaves out some interesting physical theories). We introduce a general algorithm for constructing new SO(2) invariant NED theories in the conventional approach, where only a few examples are available. We also show how to derive the Lagrangian of the SO(2) invariant theory admitting a given electrostatic solution. We further show on a simple example that some NED theories may require sources (particles) of finite (non-zero) size. Such a non-zero size source not only regularizes the infinite energy of the point charge but also satisfies the condition of regularity, that the electric field is zero at the origin. The latter condition was identified earlier as necessary and sufficient for the NED solution to generate a regular black hole via so-called double copy construction and is also satisfied by solitons. We propose a large class of solitonic NED solutions that give rise to regular black holes via double copy construction and contain solutions of Maxwell and Born-Infeld as different limits. This class of NED solutions acquires two new properties in the limit where the corresponding regular black hole’s asymptotics becomes Minkowski: it gives rise to regular higher-spin black holes via generalization of double copy — “higher-copy” construction, and for very short distances changes the sign of the force becoming repulsive/attractive for opposite/similar signs of charges.

Mantas Svazas

Solutions in Nonlinear Electrodynamics and their double copy regular black holes

In our previous article Phys. Rev. Lett. 127 (2021) 271601, we announced a novel ‘democratic’ Lagrangian formulation of general nonlinear electrodynamics in four dimensions that features electric and magnetic potentials on equal footing. Here, we give an expanded and more detailed account of this new formalism, and then proceed to push it significantly further by building the corresponding Lagrangian theories of higher form field interactions in arbitrary dimensions. Special attention is given to interactions of chiral 2k-forms in 4k + 2 dimensions, with further details for 2-forms in 6 dimensions and 4-forms in 10 dimensions. We comment more broadly on the structure of covariant equations of motion for chiral fields, and on the place of our Lagrangian theories in this context. The Lagrangian theories we develop are simple and explicit, and cover a much broader class of interactions than all past attempts in the literature.

Russia

Zhirayr Avetisyan

Thailand

Nonlinear (chiral) p-form electrodynamics

We construct a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. In the language of this Lagrangian, discrete and continuous electric-magnetic duality symmetries can be straightforwardly imposed, leading to a simple formulation for theories with the SO(2) duality invariance. When specialized to the conformally invariant case, our construction provides a manifestly duality-symmetric formulation of the recently discovered ModMax theory. We briefly comment on a natural generalization of this approach to <math><mi>p</mi></math>-forms in <math><mn>2</mn><mi>p</mi><mo>+</mo><mn>2</mn></math> dimensions.

Democratic Lagrangians for Nonlinear Electrodynamics

We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.