Four-dimensional noncommutative deformations of U(1) gauge theory and L∞ bootstrap.

We construct a family of four-dimensional noncommutative deformations of U(1) gauge theory following a general scheme, recently proposed in JHEP 08 (2020) 041 for a class of coordinate-dependent noncommutative algebras. This class includes the $$ \mathfrak{su} $$ su (2), the $$ \mathfrak{su} $$ su (1, 1) and the angular (or λ-Minkowski) noncommutative structures. We find that the presence of a fourth, commutative coordinate x0 leads to substantial novelties in the expression for the deformed field strength with respect to the corresponding three-dimensional case. The constructed field theoretical models are Poisson gauge theories, which correspond to the semi-classical limit of fully noncommutative gauge theories. Our expressions for the deformed gauge transformations, the deformed field strength and the deformed classical action exhibit flat commutative limits and they are exact in the sense that all orders in the deformation parameter are present. We review the connection of the formalism with the L∞ bootstrap and with symplectic embeddings, and derive the L∞-algebra, which underlies our model.

Ostrogradsky–Hamilton approach to geodetic brane gravity

In this paper, we develop the Ostrogradsky–Hamilton formalism for geodetic brane gravity, described by the Regge–Teitelboim geometric model in higher codimension. We treat this gravity theory as a second-order derivative theory, based on the extrinsic geometric structure of the model. As opposed to previous treatments of geodetic brane gravity, our Lagrangian is linearly dependent on second-order time derivatives of the field variables, the embedding functions. The difference resides in a boundary term in the action, usually discarded. Certainly, this suggests applying an appropriate Ostrogradsky–Hamiltonian approach to this type of theories. The price to pay for this choice is the appearance of second-class constraints. We determine the full set of phase space constraints, as well as the gauge transformations they generate in the reduced phase space. Additionally, we compute the algebra of constraints and explain its physical content. In the same spirit, we deduce the counting of the physical degrees of freedom. We comment briefly on the naive formal canonical quantization emerging from our development.

Conserved laws and dynamical structure of axions coupled to photons

In this work, we carry out a study of the conserved quantities and dynamical structure of the four-dimensional modified axion electrodynamics theory described by the axion-photon coupling. In the first part of the analysis, we employ the covariant phase space method to construct the conserved currents and to derive the Noether charges associated with the gauge symmetry of the theory. We further derive the improved energy–momentum tensor using the Belinfante–Rosenfeld procedure, which leads us to the expressions for the energy, momentum, and energy flux densities. Thereafter, with the help of Faddeev–Jackiw’s Hamiltonian reduction formalism, we obtain the relevant fundamental brackets structure for the dynamic variables and the functional measure for determining the quantum transition amplitude. We also confirm that modified axion electrodynamics has three physical degrees of freedom per space point. Moreover, using this symplectic framework, we yield the gauge transformations and the structure of the constraints directly from the zero-modes of the corresponding pre-symplectic matrix.

A Systematic Approach to Consistent Truncations of Supergravity Theories

Exceptional generalised geometry is a reformulation of eleven/ten-dimensional supergravity that unifies ordinary diffeomorphisms and gauge transformations of the higher-rank potentials of the theory in an extended notion of diffeormorphisms. These features make exceptional generalised geometry a very powerful tool to study consistent truncations of eleven/ten-dimensional supergravities. In this article, we review how the notion of generalised G-structure allows us to derive consistent truncations to supergravity theories in various dimensions and with different amounts of supersymmetry. We discuss in detail the truncations of eleven-dimensional supergravity to N=4 and N=2 supergravity in five dimensions.

Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry

We formulate general definitions of semi-classical gauge transformations for noncommutative gauge theories in general backgrounds of string theory, and give novel explicit constructions using techniques based on symplectic embeddings of almost Poisson structures. In the absence of fluxes the gauge symmetries close a Poisson gauge algebra and their action is governed by a $P_\infty$-algebra which we construct explicitly from the symplectic embedding. In curved backgrounds they close a field dependent gauge algebra governed by an $L_\infty$-algebra which is not a $P_\infty$-algebra. Our technique produces new all orders constructions which are significantly simpler compared to previous approaches, and we illustrate its applicability in several examples of interest in noncommutative field theory and gravity. We further show that our symplectic embeddings naturally define a $P_\infty$-structure on the exterior algebra of differential forms on a generic almost Poisson manifold, which generalizes earlier constructions of differential graded Poisson algebras, and suggests a new approach to defining noncommutative gauge theories beyond the gauge sector and the semi-classical limit based on $A_\infty$-algebras.

Note on the bundle geometry of field space, variational connections, the dressing field method, & presymplectic structures of gauge theories over bounded regions

In this note, we consider how the bundle geometry of field space interplays with the covariant phase space methods so as to allow to write results of some generality on the presymplectic structure of invariant gauge theories coupled to matter. We obtain in particular the generic form of Noether charges associated with field-independent and field-dependent gauge parameters, as well as their Poisson bracket. We also provide the general field-dependent gauge transformations of the presymplectic potential and 2-form, which clearly highlights the problem posed by boundaries in generic situations. We then conduct a comparative analysis of two strategies recently considered to evade the boundary problem and associate a modified symplectic structure to a gauge theory over a bounded region: namely the use of edge modes on the one hand, and of variational connections on the other. To do so, we first try to give the clearest geometric account of both, showing in particular that edge modes are a special case of a differential geometric tool of gauge symmetry reduction known as the “dressing field method”. Applications to Yang-Mills theory and General Relativity reproduce or generalise several results of the recent literature.

On the double copy for spinning matter

We explore various tree-level double copy constructions for amplitudes including massive particles with spin. By working in general dimensions, we use that particles with spins s ≤ 2 are fundamental to argue that the corresponding double copy relations partially follow from compactification of their massless counterparts. This massless origin fixes the coupling of gluons, dilatons and axions to matter in a characteristic way (for instance fixing the gyromagnetic ratio), whereas the graviton couples universally reflecting the equivalence principle. For spin-1 matter we conjecture all-order Lagrangians reproducing the interactions with up to two massive lines and we test them in a classical setup, where the massive lines represent spinning compact objects such as black holes. We also test the amplitudes via CHY formulae for both bosonic and fermionic integrands. At five points, we show that by applying generalized gauge transformations one can obtain a smooth transition from quantum to classical BCJ double copy relations for radiation, thereby providing a QFT derivation for the latter. As an application, we show how the theory arising in the classical double copy of Goldberger and Ridgway can be naturally identified with a certain compactification of $$ \mathcal{N} $$ N = 4 Supergravity.

A low-energy limit of Yang-Mills theory on de Sitter space

We consider Yang-Mills theory with a compact structure group G on four-dimensional de Sitter space dS4. Using conformal invariance, we transform the theory from dS4 to the finite cylinder $$ \mathcal{I} $$ I × S3, where $$ \mathcal{I} $$ I = (−π/2, π/2) and S3 is the round three-sphere. By considering only bundles P → $$ \mathcal{I} $$ I × S3 which are framed over the temporal boundary ∂$$ \mathcal{I} $$ I × S3, we introduce additional degrees of freedom which restrict gauge transformations to be identity on ∂$$ \mathcal{I} $$ I × S3. We study the consequences of the framing on the variation of the action, and on the Yang-Mills equations. This allows for an infinite-dimensional moduli space of Yang-Mills vacua on dS4. We show that, in the low-energy limit, when momentum along $$ \mathcal{I} $$ I is much smaller than along S3, the Yang-Mills dynamics in dS4 is approximated by geodesic motion in the infinite-dimensional space $$ \mathcal{M} $$ M vac of gauge-inequivalent Yang-Mills vacua on S3. Since $$ \mathcal{M} $$ M vac ≅ C∞(S3, G)/G is a group manifold, the dynamics is expected to be integrable.

Superspace first order formalism, trivial symmetries and electromagnetic interactions of linearized supergravity

We introduce a first order description of linearized non-minimal (n = −1) supergravity in superspace, using the unconstrained prepotential superfield instead of the conventionally constrained super one forms. In this description, after integrating out the connection-like auxiliary superfield of first-order formalism, the superspace action is expressed in terms of a single superfield which combines the prepotential and compensator superfields. We use this description to construct the supersymmetric cubic interaction vertex 3/2 − 3/2 − 1/2 which describes the electromagnetic interaction between two non-minimal supergravity multiplets (superspin Y = 3/2 which contains a spin 2 and a spin 3/2 particles) and a vector multiplet (superspin Y = 1/2 contains a spin 1 and a spin 1/2 particles). Exploring the trivial symmetries emerging between the two Y = 3/2 supermultiplets, we show that this cubic vertex must depend on the vector multiplet superfield strength. This result generalize previous results for non-supersymmetric electromagnetic interactions of spin 2 particles. The constructed cubic interaction generates non-trivial deformations of the gauge transformations.

Poisson gauge theory

The Poisson gauge algebra is a semi-classical limit of complete non- commutative gauge algebra. In the present work we formulate the Poisson gauge theory which is a dynamical field theoretical model having the Poisson gauge algebra as a corresponding algebra of gauge symmetries. The proposed model is designed to investigate the semi-classical features of the full non-commutative gauge theory with coordinate dependent non-commutativity Θab(x), especially whose with a non-constant rank. We derive the expression for the covariant derivative of matter field. The commutator relation for the covariant derivatives defines the Poisson field strength which is covariant under the Poisson gauge transformations and reproduces the standard U(1) field strength in the commutative limit. We derive the corresponding Bianchi identities. The field equations for the gauge and the matter fields are obtained from the gauge invariant action. We consider different examples of linear in coordinates Poisson structures Θab(x), as well as non-linear ones, and obtain explicit expressions for all proposed constructions. Our model is unique up to invertible field redefinitions and coordinate transformations.