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We compute the conserved charges associated with the asymptotic symmetries of massless particles by examining their free theory in Minkowski space–time. We give a procedure to systematically deduce the fall off of the massless fields at spatial infinity and show that it has a universal behavior when expressed in tangent space. We do this for generic massless particles. We do not impose gauge fixing conditions, which will allow us to uncover new nonzero charges for the graviton beyond the well-known supertranslation charges. We also compute conserved charges in the dual formulations of certain low-spin particles and argue that this leads to an infinite number of new conserved charges. [ABSTRACT FROM AUTHOR]

In this paper, we study the holographic complexity of rotating Banados–Teitelboim–Zanelli black hole in the context of the "Complexity-Action" conjecture and in the framework of General Minimal Massive Gravity (GMMG) and Exotic General Massive Gravity (EGMG). In addition, we investigate the action growth rate based on two kinds of conserved charges of the theories and examine the Lloyd bound on the rate of quantum computation. Then, we study the complexity of the formation of black holes in both theories. [ABSTRACT FROM AUTHOR]

We derive the conserved currents and potentials for Einstein gravity on the basis of a recently proposed connection-independent formulation of this theory. Particularly, we obtain a superpotential that generalizes naturally the usual Katz–Bicak–Lynden–Bell (KBL) one by including the contribution from an arbitrary reference affine connection. The potentials can be adopted to define conserved charges of Einstein gravity. By contrast with the usual metric formulation described by the Einstein–Hilbert Lagrangian, our analysis reveals that the connection-independent formulation conveniently reproduces the KBL superpotential and it can provide a unified description for conserved charges defined by virtue of the KBL method and the covariant phase space approach. In addition, we investigate the properties of the connection-independent Lagrangian under connection and conformal transformations, and we reveal that the connection-independent Lagrangian can be reproduced by converting the Levi-Civita connection in the boundary term into an arbitrary one in terms of the Gamma squared expression for the Einstein–Hilbert Lagrangian. [ABSTRACT FROM AUTHOR]

We show that the laws of electromagnetism in (D + 1) -dimensional Minkowski space-time M , explicitly for D = 1 , 2 and 3, can be obtained from an integral representation of the zero-curvature equation in the corresponding loop space L (D - 1) (M) . The conservation of the electric charge can be seen as the result of a hidden symmetry in this representation of the dynamical equations. [ABSTRACT FROM AUTHOR]

The off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetries are obtained by using the (anti-)chiral superfield approach (ACSA) to Becchi–Rouet–Stora–Tyutin (BRST) formalism for the four (3 + 1) -dimensional (4D) Stückelberg-modified massive Abelian 2-form gauge theory. We perform exactly similar kind of exercise for the derivation of the off-shell nilpotent (anti-)co-BRST symmetry transformations, too. In the above derivations, the symmetry invariant restrictions on the superfields play very important and decisive roles. To prove the sanctity of the above nilpotent symmetries, we generalize our 4D ordinary theory (defined on the 4D flat Minkowskian space–time manifold) to its counterparts (4 , 1) -dimensional (anti-)chiral super-submanifolds of the (4 , 2) -dimensional supermanifold which is parametrized by the superspace coordinates Z M = (x μ , , ̄) where x μ (μ = 0 , 1 , 2 , 3) are the bosonic coordinates and a pair of Grassmannian variables (, ̄) are fermionic: 2 = 2 ̄ = 0 , ̄ + ̄ = 0 in nature. One of the novel observations of our present endeavor is the derivation of the Curci–Ferrari (CF)-type restrictions from the requirement of the symmetry invariance of the coupled (but equivalent) Lagrangian densities of our theory within the framework of ACSA to BRST formalism. We also exploit the standard techniques of ACSA to capture the off-shell nilpotency and absolute anticommutativity of the conserved (anti-)BRST as well as the conserved (anti-)co-BRST charges. In a subtle manner, the proof of the absolute anticommutativity of the above conserved charges also implies the existence of the appropriate CF-type restrictions on our theory. This proof is also a novel result. [ABSTRACT FROM AUTHOR]

We discuss the nilpotent Becchi–Rouet–Stora–Tyutin (BRST), anti-BRST and (anti-) co-BRST symmetry transformations and derive their corresponding conserved charges in the case of a two (1 + 1) -dimensional (2D) self-interacting non-Abelian gauge theory (without any interaction with matter fields). We point out a set of novel features that emerge out in the BRST and co-BRST analysis of the above 2D gauge theory. The algebraic structures of the symmetry operators (and corresponding conserved charges) and their relationship with the cohomological operators of differential geometry are established too. To be more precise, we demonstrate the existence of a single Lagrangian density that respects the continuous symmetries which obey proper algebraic structure of the cohomological operators of differential geometry. In the literature, such observations have been made for the coupled (but equivalent) Lagrangian densities of the 4D non-Abelian gauge theory. We lay emphasis on the existence and properties of the Curci–Ferrari (CF)-type restrictions in the context of (anti-)BRST and (anti-)co-BRST symmetry transformations and pinpoint their key differences and similarities. All the observations, connected with the (anti-)co-BRST symmetries, are completely novel. [ABSTRACT FROM AUTHOR]

Recently, it was shown that the conserved charges of asymptotically anti-de Sitter spacetimes can be written in an explicitly gauge-invariant way in terms of the linearized Riemann tensor and the Killing vectors. Here, we employ this construction to compute the mass and angular momenta of the D -dimensional Kerr-AdS black holes, which is one of the most remarkable Einstein metrics generalizing the four-dimensional rotating black hole. [ABSTRACT FROM AUTHOR]

In general relativity, finding out the geodesics of a given spacetime manifold is an important task because it determines which classical processes are dynamically forbidden. Conserved quantities play an important role in solving the geodesic equations of a general spacetime manifold. Furthermore, knowing all possible conserved quantities of a system gives information about the hidden symmetries of that system since conserved quantities are deeply connected with the symmetries of the system. These are very important in their own right. Conserved quantities are also useful to capture certain features of spacetime manifold for an asymptotic observer. In this article, we show the existence of these conserved charges and their algebra in a generic curved spacetime for a class of dynamical systems with the Hamiltonians quadratic and linear in momentum and spin. [ABSTRACT FROM AUTHOR]

Recently a new approach in constructing the conserved charges in cosmological Einstein gravity was given. In this new formulation, instead of using the explicit form of the field equations, a covariantly conserved rank-four tensor was used. In the resulting charge expression, instead of the first derivative of the metric perturbation, the linearized Riemann tensor appears along with the derivative of the background Killing vector fields. Here we give a detailed analysis of the first-order and the second-order perturbation theory in a gauge-invariant form in cosmological Einstein gravity. The linearized Einstein tensor is gauge-invariant at the first order but it is not so at the second order, which complicates the discussion. This method depends on the assumption that the first-order metric perturbation can be decomposed into gauge-variant and gauge-invariant parts and the gauge-variant parts do not contribute to physical quantities. [ABSTRACT FROM AUTHOR]

We derive the off-shell nilpotent (fermionic) (anti-)BRST symmetry transformations by exploiting the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism for the interacting Abelian 1-form gauge theories where there is a coupling between the U(1) Abelian 1-form gauge field and Dirac as well as complex scalar fields. We exploit the (anti-)BRST invariant restrictions on the (anti-)chiral superfields to derive the fermionic symmetries of our present D-dimensional Abelian 1-form gauge theories. The novel observation of our present investigation is the derivation of the absolute anticommutativity of the nilpotent (anti-)BRST charges despite the fact that our ordinary D-dimensional theories are generalized onto the ( D,1)-dimensional (anti-) chiral super-submanifolds (of the general ( D,2)-dimensional supermanifold) where only the (anti-)chiral super expansions of the (anti-)chiral superfields have been taken into account. We also discuss the nilpotency of the (anti-)BRST charges and (anti-)BRST invariance of the Lagrangian densities of our present theories within the framework of ACSA to BRST formalism. [ABSTRACT FROM AUTHOR]

Recently, a general method for calculating conserved charges for (black hole) solutions to generally covariant gravitational theories, in any dimensions and with arbitrary asymptotic behaviors has been introduced. Equipped with this method, which can be dubbed as 'solution phase space method,' we calculate mass and angular momentum for the Kerr-dS black holes. Furthermore, for any choice of horizons, associated entropy and the first law of thermodynamics are derived. Interestingly, according to insensitivity of the analysis to the chosen cosmological constant, the analysis unifies the thermodynamics of rotating stationary black holes in 4 (and other) dimensions with either AdS, flat or dS asymptotics. We extend the analysis to include electric charge, i.e. to the Kerr-Newman-dS black holes. [ABSTRACT FROM AUTHOR]

Conserved currents of any spin t > 0 built from bosonic symmetric massless gauge fields of arbitrary integer spins s 1 + s 2 > t in A d S 4 are found. Analogous to the case of 4 d Minkowski space, currents considered in this paper are not gauge invariant, but generate gauge-invariant conserved charges.

We extend the Abbott–Deser–Tekin (ADT) method to the computation of the global charges associated with Killing vectors of the background for solutions of general minimal massive gravity (GMMG) linearized about an arbitrary background. Then, we implement our result in various solutions to evaluate the mass and angular momentum with arbitrary asymptotics. [ABSTRACT FROM AUTHOR]

We study models where the gauge coupling constants, masses and the gravitational constant are functions of some conserved charge in the universe, and furthermore a cosmological constant that depends on the total charge of the universe. We first consider the standard Dirac action, but where the mass and the electromagnetic coupling constant are a function of the charge in the universe and afterwards extend this to curved spacetime and consider gauge coupling constants, the gravitational constant and the mass as a function of the charge of the universe, which represent a sort of Mach principle for all the constants of nature. In the flat space formulation, the formalism is not manifestly Lorentz invariant, however Lorentz invariance can be restored by performing a phase transformation of the Dirac field. One interesting model of this type is one where the action is invariant under rescalings of the Dirac wave function. In the curved space time formulation, there is the additional feature that some of the equations of motion break the general coordinate invariance also, but in a way that can be understood as a coordinate choice only, so the equations are still of the General Relativity type, but with a certain natural coordinate choice, where there is no current of the charge. We have generalized what we have done and also constructed a cosmological constant which depends on the total charge of the universe. We discuss how these ideas work when the space where the charges live is finite. If we were to use some only approximately conserved charge for these constructions, like say baryon number (in the context of the standard model), this will lead to corresponding violations of Lorentz symmetry in the early universe for example. We also briefly discuss another non-local formulations where the coupling constants are functions of the Pontryagin index of some non-abelian gauge field configurations. The construction of charge dependent contributions can also be motivated from the structure of the 'infra-red counter terms' needed to cancel infra red divergences for example in three dimensions. [ABSTRACT FROM AUTHOR]

Some unusual relations between stress tensors, conservation and equations of motion are briefly reviewed. [ABSTRACT FROM AUTHOR]