We consider a class of models in even spacetime dimensions 2$\textit{n}$ which share many similarities with Chern-Simons theories in odd spacetime dimensions 2$\textit{n}$ + 1. The independent dynamical variables of these models are a GL(2$\textit{n}$)-connection and a metric in internal space. The action is a polynomial of degree $\textit{n}$ in the curvature of the connection, with indices saturated by means of the metric and the Levi-Civita tensor. We show that the theory has no local degree of freedom in 2 spacetime dimensions ($\textit{n}$ = 1), where it can be reformulated as a constrained $\textit{BF}$ model, but that its dynamics is more intrincate in higher dimensions ($\textit{n >}$ 1), where local degrees of freedom are present. We treat in detail the cases of 2 and 4 spacetime dimensions.

Chile

Máximo Bañados

Belgium

France

Marc Henneaux

Palatini Gauss-Bonnet theory

<p>We propose an alternative description of generalized unimodular gravity, extending the Henneaux-Teitelboim approach to unimodular gravity. The central feature of this formulation is the consistent incorporation of time reparametrization, which enhances the gauge structure and reveals a spatial nonlocality hidden in the dynamics of the original formulation. We examine the resulting dynamics, emphasizing the effects of spatial nonlocality, and outline the constraint structure. We show that the gauge symmetry in the gravitational sector is extended by a functionally incomplete symmetry, as occurs in the unimodular gravity. However, in contrast to the latter, the resulting action is not fully diffeomorphism invariant.</p>

Russia

Dmitry Nesterov

Ksenia Lyamkina

Henneaux-Teitelboim form of the generalized unimodular gravity action

We provide a new perspective on the general matching conditions between the future of past null infinity and the past of future null infinity, emphasizing the impact of dominant logarithmic terms in the asymptotic expansion of the fields near null infinity. We explicitly consider the cases of a massless scalar field and of electromagnetism. Key in our derivation is the identification of the physical origin of these logarithms, which are associated with advanced and retarded radiation saturating the finite energy flux condition at null infinity (in a space of functions which is made precise). The matching conditions arise then from the requirement of Coulombic (i.e., 1$\textit{/r}$) behaviour at spatial infinity.

Matías Briceño

Hernán González

Austria

Alfredo Pérez

Matching conditions at null infinity in the presence of logarithms: the role of advanced and retarded radiation

The BRST Noether theorem, or “Noether’s 1$\textit{.}$5 theorem”, asserts the triviality of the BRST Noether current. We provide two proofs of this theorem that are both valid without restriction on the structure of the gauge theory, extending thereby previous proofs holding in the case of gauge theories for which the solution of the master equation is linear in the antifields. We also relate explicitly the BRST Noether current to the BRST master current appearing in the master equation.

Glenn Barnich

Laurent Baulieu

Japan

Tom Wetzstein

BV-BRST Noether theorem

<p>The Hamiltonian formulation of the BMS symmetry on spacelike hypersurfaces enables one to define its action on solutions of the Wheeler-DeWitt equation. Using the Becchi-Rouet-Stora-Tyutin (BRST) reformulation of the theory, we provide operator expressions for the matrix elements of the BMS operators between Wheeler-DeWitt states. To that end, we construct the BRST-invariant extensions of the BMS generators, which form a BRST extension of the BMS algebra.</p>

Wheeler-DeWitt Equation and Bondi-Metzner-Sachs (BMS) Symmetry

Logarithmic angle-dependent gauge transformations are symmetries of electromagnetism that are canonically conjugate to the standard $$ \mathcal{O}(1) $$ angle-dependent $\textit{u}$(1) transformations. They were exhibited a few years ago at spatial infinity. In this paper, we derive their explicit form at null infinity. We also derive the expression there of the associated “conserved” surface integrals. To that end, we provide a comprehensive analysis of the behaviour of the electromagnetic vector potential $\textit{A}$ in the vicinity of null infinity for generic initial conditions given on a Cauchy hypersurface. This behaviour is given by a polylogarithmic expansion involving both gauge-invariant logarithmic terms also present in the field strengths and gauge-variant logarithmic terms with physical content, which we identify. We show on which explicit terms, and how, do the logarithmic angle-dependent gauge transformations act. Other results of this paper are a derivation of the matching conditions for the Goldstone boson and for the conserved charges of the angle-dependent $\textit{u}$(1) asymptotic symmetries, as well as a clarification of a misconception concerning the non-existence of these angle-dependent $\textit{u}$(1) charges in the presence of logarithms at null infinity. We also briefly comment on higher spacetime dimensions.

Oscar Fuentealba

Logarithmic angle-dependent gauge transformations at null infinity

Matching conditions relating the fields at the future of past null infinity with the fields at the past of future null infinity play a central role in the analysis of asymptotic symmetries and conservation laws in asymptotically flat spacetimes. These matching conditions can be derived from initial data given on a Cauchy hypersurface by integrating forward and backward in time the field equations to leading order in an asymptotic expansion, all the way to future and past null infinities. The standard matching conditions considered in the literature are valid only in the case when the expansion near null infinity (which is generically polylogarithmic) has no dominant logarithmic term. The absence of dominant logarithmic term, in turn, holds only when the leading order of the initial conditions on a Cauchy hypersurface (which contains no logarithm) fulfills definite parity conditions under the antipodal map of the sphere at infinity. One can consistently consider opposite parity conditions. While these do not conflict with the asymptotic symmetry group, they lead to a very different asymptotic behaviour near null infinity, where the expansion starts now with logarithmic terms that are no longer subdominant (even though such logarithmic terms are absent in the initial data), which implies different matching conditions.

Logarithmic matching between past infinity and future infinity: The massless scalar field in Minkowski space

We analyse the asymptotic symmetries of electromagnetism non-minimally coupled to scalar fields, with non-minimal couplings of the Fermi type that occur in extended supergravity models. Our study is carried out at spatial infinity where minimal and non-minimal couplings exhibit very different asymptotic properties: while the former generically cannot be neglected at infinity, the latter can. Electromagnetic non-minimal couplings are in that respect similar to gravitational minimal couplings, which are also asymptotically subdominant. Because the non-minimally interacting model is asymptotic to the free one, its asymptotic symmetries are the same as the ones of the free theory, i.e., described by angle-dependent u(1) gauge transformations. We also analyse the duality symmetry and show that it is broken to its compact subgroup by the asymptotic conditions. Finally, we consider logarithmic gauge transformations and use them to simplify the symmetry algebra.

Jules Mas

Non-minimal couplings to U(1)-gauge fields and asymptotic symmetries

We construct Carroll-invariant theories with fields propagating outside the Carroll light cone, i.e., at a speed strictly greater than zero (“Carroll swiftons”). We first consider models in flat Carroll spacetime in general dimensions, where we present scalar and vector Carroll swifton field theories. We then turn to the coupling to gravity and achieve in particular in two dimensions a Carroll-invariant scalar swifton by coupling it suitably to Carroll dilaton gravity. Its backreaction on the geometry generates dynamical torsion.

Florian Ecker

Daniel Grumiller

Patricio Salgado-Rebolledo

Carroll-invariant propagating fields

We show that the non-linear BMS5 symmetry algebra of asymptotically flat Einstein gravity in five dimensions, as well as the super-BMS4 superalgebra of asymptotically flat supergravity, can be redefined so as to take a direct sum structure. In the new presentation of the (super-)algebra, angle-dependent translations and angle-dependent supersymmetry transformations commute with the (super-)Poincaré generators. We also explain in detail the structure and charge-integrability of asymptotic symmetries with symmetry parameters depending on the fields (through the charges themselves), a topic relevant for nonlinear asymptotic symmetry algebras.