<p>Motivated by the work of Longhi and Materassi, who constructed a realization of the (centerless) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>BMS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> algebra for the massive Klein-Gordon field in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mo>+</mo><mn>1</mn></math> dimensions, we build a realization of the (centerless) massless <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>BMS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> algebra including superrotations. This realization depends only on the momenta in the light cone expressed in celestial coordinates without any reference to the Klein-Gordon field. The quadratic Casimir of the Lorentz algebra is written in terms of a second order differential operator and the volume form plays an essential role in this construction. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>BMS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> algebra in terms of vector fields shows its kinematical nature, like the Poincaré algebra. We also construct a dynamical realization of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>BMS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> from the symplectic structure on the solutions of the massless four-dimensional Klein-Gordon field in terms of quadratic expressions of the Fourier modes and plane waves invariant under translations. Using the Mellin transform, we rewrite the Klein-Gordon field in terms of the boost invariant basis, and write down the corresponding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>BMS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> realization. We also provide the relation with spherical harmonics, linking our results with the solutions of Longhi-Materassi, which are in fact a subset of ours.</p>

Spain

Carles Batlle

Italy

Roberto Casalbuoni

Daniele Dominici

United Kingdom

José Figueroa-O’Farrill

Joaquim Gomis

Celestial kinematical interpretation for an extended <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>BMS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> algebra

<p>Starting from the isomorphism between the anti–de Sitter (AdS) Carroll and Poincaré algebras, we obtain the magnetic AdS Carroll gravity in three dimensions. Moreover, we derive the first set of asymptotic conditions for the AdS Carroll structure, and we prove that the asymptotic symmetry algebra is given by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="fraktur">bms</mi><mn>3</mn></msub></math> algebra. By mapping the three-dimensional asymptotically flat solutions of Poincaré gravity into an AdS Carroll spacetime, we demonstrate that the resulting solutions satisfy the field equations of the Chern-Simons formulation of AdS Carroll gravity, and we note that this solution possesses an infinite set of Killing vectors.</p>

Chile

Luis Avilés

Iceland

Diego Hidalgo

Omar Valdivia

AdS Carroll structures from Poincaré isomorphism: Asymptotic symmetry analysis

We construct new Carroll strings in flat space by considering the Carroll limit of equivalent relativistic string theories at the classical level. In the limit these Carroll strings are no longer equivalent and have different degrees of freedom. This fact is due to a general phenomenon that the configuration space and canonical Lagrangians are no longer equivalent after a singular redefinition of the variables and of the parameters of the starting Lagrangians.

Nonequivalence of Carroll limits in relativistic string theory

We study the bosonic sector of a decoupling limit of type IIA superstring theory, where a background Ramond-Ramond one-form is fined tuned to its critical value, such that it cancels the associated background D0-brane tension. The light excitations in this critical limit are D0-branes, whose dynamics is described by the Banks-Fischler-Shenker-Susskind (BFSS) Matrix theory that corresponds to M-theory in the Discrete Light-Cone Quantization (DLCQ). We develop the worldsheet formalism for the fundamental string in the same critical limit of type IIA superstring theory. We show that the fundamental string develops singularities on its worldsheet, whose topology is described by nodal Riemann spheres as in ambitwistor string theory. We study the T-duality transformations of this string sigma model and provide a worldsheet derivation for the recently revived and expanded duality web that unifies a zoo of decoupling limits in type II superstring theories. By matching the string worldsheet actions, we demonstrate how some of these decoupling limits are related to tensionless (and ambitwistor) string theory, Carrollian string theory, the Spin Matrix limits of the AdS/CFT correspondence, and more.

Sweden

Ziqi Yan

Worldsheet formalism for decoupling limits in string theory

The free massless superparticle is reanalyzed, in particular by performing the Gupta-Bleuler quantization, using the first- and second-class constraints of the model, and obtaining as a result, the Weyl equation for the spinorial component of the chiral superfield. Then we construct a superconformal model of two interacting massless superparticles from the free case by the introduction of an invariant interaction. The interaction introduces an effective mass for each particle by modifying the structure of fermionic constraints, all becoming second class. The quantization of the model produces a bilocal chiral superfield. We also generalize the model by considering a system of superconformal interacting particles and its continuum limit.

Superconformal interacting particles

The (pre)multisymplectic geometry of the De Donder–Weyl formalism for field theories is further developed for a variety of field theories including a scalar field theory from the canonical Klein-Gordon action, the electric and magnetic Carrollian scalar field theories, bosonic string theory from the Nambu-Goto action, and <math><mn>2</mn><mo>+</mo><mn>1</mn></math> gravity as a Chern-Simons theory. The Lagrangians for the scalar field theories and for <math><mn>2</mn><mo>+</mo><mn>1</mn></math> Chern-Simons gravity are found to be singular in the De Donder–Weyl sense while the Nambu-Goto Lagrangian is found to be regular. Furthermore, the constraint structure of the premultisymplectic phase spaces of singular field theories is explained and applied to these theories. Finally, it is studied how symmetries are developed on the (pre)multisymplectic phase spaces in the presence of constraints.

Arnoldo Guerra

Narciso Román-Roy

Multisymplectic constraint analysis of scalar field theories, Chern-Simons gravity, and bosonic string theory

We consider non-Lorentzian expansions, Galilean and Carrollian, of the Lorentz force equation in which both the particle position and the electro-magnetic field are expanded. There are two well-known limits in the case of a constant field, called electric and magnetic, that are studied separately. We show that the resulting equations of motion follow equivalently from considering a non-linear realisation of a certain infinite-dimensional algebras.

José Cerdeira

Germany

Belgium

Axel Kleinschmidt

Non-Lorentzian expansions of the Lorentz force and kinematical algebras

We construct a Lorentz invariant massive particle model in (2+1) space-time with an enlarged set of symmetries which includes Bondi-Metzner-Sachs (BMS) translations (supertranslations), using the non-linear realization framework. The Hamiltonian formalism for the resulting Lagrangian is constructed, and the infinite phase-space constraints and the set of gauge transformations are analysed. We also compute the massless limit of the theory in phase-space. After eliminating the gauge degrees of freedom, the physical reduced space is left only with the degrees of freedom of a standard Poincaré particle but with a residual set of symmetries that we prove to be BMS. A similar result for the massless limit, including in this case superrotations, is pointed out.

Víctor Campello

Particle realization of Bondi-Metzner-Sachs symmetry in 2 + 1 space-time

In this paper we analyze two different models of two interacting conformal Carroll particles that can be obtained as the Carrollian limit of two relativistic conformal particles. The first model describes particles with zero velocity and exhibits infinite dimensional symmetries which are reminiscent of the BMS symmetries. A second model of interaction of Carrollian particles is proposed, where the particles have nonzero velocity and therefore, as a consequence of the limit <math><mi>c</mi><mo>→</mo><mn>0</mn></math>, are tachyons. Infinite dimensional symmetries are present also in this model.

Two interacting conformal Carroll particles

We construct the electric and magnetic Newton-Hooke and Carroll Jackiw-Teitelboim gravity theories using the isomorphism of Newton-Hooke ±  and (A-)dS Carroll algebras in (1+1)-spacetime dimensions. The starting point is the non-relativistic and Carroll version of Jackiw-Teitelboim gravity without restrictions on the geometry studied in [1].