Flat Space Research Articles

BMS field theories with u(1) symmetry

We investigate quantum field theories in two dimensions (2D) with an underlying Bondi--van der Burgh--Metzner-Sachs symmetry augmented by $\mathfrak{u}(1)$ currents. These field theories are expected to holographically capture features of charged versions of cosmological solutions in asymptotically flat 3D spacetimes called flat space cosmologies. We conduct a study of the modular properties of these field theories. The characters for the highest weight representations of the symmetry algebra are constructed, and the partition function of the theory is obtained from them. We derive the density of (primary) states and find the entropy and asymptotic values of the structure constants exploiting the modular properties of the partition function and the torus one-point function. The expression for the asymptotic structure constants shows shifts in the weights and one of the central terms and an extra phase compared to the earlier results in the literature for Bondi--van der Burgh--Metzner-Sachs invariant theories without $\mathfrak{u}(1)$ currents present. We reproduce our field results for the structure constants by a bulk computation involving a scalar probe in the background of a charged flat space cosmology.

Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ

We present an analysis of the perturbative realization of the TTJJ correlator, with two stress energy tensors and two conserved currents, using free field theory, integrating out conformal sectors in the quantum corrections. This allows to define, around flat space, an exact perturbative expansion of the complete anomaly effective action – up to 4-point functions – whose predictions can be compared against those of the anomaly induced action. The latter is a variational solution of the conformal anomaly constraint at d=4 in the form of a nonlocal Wess–Zumino action. The renormalization procedure and the degeneracies of the tensor structures of this correlator are discussed, valid for a generic conformal field theory, deriving its anomalous trace Ward identities (WIs). In this application, we also illustrate a general procedure that identifies the minimal number of tensorial structures and corresponding form factors for the TTJJ and any 4-point function. The approach is implemented for three, four and five dimensions, addressing the tensor degeneracies of the expansion in momentum space. We show that the renormalized TTJJ can be split into two contributions, a non anomalous and an anomalous part, each separately conserved. The first satisfies ordinary trace WIs, while the second satisfies anomalous trace WIs. The result of the direct computation is compared against the expression of the same 4-point function derived from the nonlocal anomaly induced action. We show that the prediction for the anomalous part of the TTJJ derived from such action, evaluated in two different conformal decompositions, the Riegert and Fradkin–Vilkovisky (FV) choices, differ from the anomaly part identified in the perturbative TTJJ, in the flat spacetime limit. The anomaly part of the correlator computed with the Riegert choice is affected by double poles, while the one computed with the FV choice does not satisfy the conservation WIs. We present the correct form of the expansion of the anomaly induced action at the second order in the metric perturbations around flat space that reproduces the perturbative result.

Chiral current induced by torsional Weyl anomaly

Torsion can be realized as dislocation in the crystal lattice of material. It is particularly interesting if the material has fermions in the spectrum, such as graphene, topological insulators, and Dirac and Weyl semimetals, as it's transport properties can be affected by the torsion. In this paper, we find that, due to Weyl anomaly, torsion in Dirac and Weyl semimetals can induce novel chiral currents, either near a boundary or in a ``conformally flat space.'' We briefly discuss how to measure this interesting effect in experiment. It is remarkable that these experiments can help to clarify the theoretical controversy of whether an imaginary Pontryagin density could appear in the Weyl anomaly.

Gravitational wave memory in conformally flat spacetimes

We study the gravitational wave memory effect in spacetimes related to flat space by a conformal transformation. The discussion is general but the gravitational wave length scale is assumed to be small compared with the background curvature radius. The general formulas are applied to Friedmann-Robertson-Walker metrics of all spatial curvatures. The effect of new terms stemming from spatial curvature is potentially detectable in future gravitational wave measurements.

PSO-Based Sparse Source Location in Large-Scale Environments With a UAV Swarm

Locating multiple sources in an unknown environment based on their signal strength is called a multi-source location problem. In recent years, there has been great interest in deploying autonomous devices to solve it. A particle swarm optimizer (PSO) is a widely employed source location method. Yet most work in this field focuses on a flat search space while ignoring height information. An unmanned aerial vehicle (UAV) has a coarser but wider view as it flies higher. Inspired by such facts, this paper focuses on improving the efficiency of locating sources by utilizing height information through UAVs. A novel source location model is designed where their sensing range gradually increases as their flying height rises, but their obtained signal strength fades away. It can be directly deployed to existing PSO-based multi-source location methods and improve their performance, especially in a large-scale environment with sparse sources. UAVs can spontaneously switch their search schemes between a rough search at a higher height and a fine one at a lower height. Experimental results of three PSO-based methods show their significant improvement after deploying our model. Given the same computation resources, its deployment leads to over 30% hike in both location accuracy and speed. This represents a great advance to the field of source location.

Particles of Negative and Zero Energy in Black Holes and Cosmological Models

Particles with negative energies are considered for three different cases: inside the horizon of a Schwarzschild black hole, Milne’s coordinates in flat Minkowski space–time (Milne’s universe using nonsynchronous coordinates) and in the cosmological Gödel model of the rotating universe. It is shown that, differently from the Gödel model with a nondiagonal term, where it occurs that negative energies are impossible, they are present in all other cases considered in the paper. Particles with zero energy are also possible in the first two cases.

A spherically symmetric gravitational solution of nearly conformally flat metric measure space

In this manuscript, we study the nearly flat approximation of a conformally invariant gravitational theory in metric measure space (MMS). In addition, we investigate the transformation of the energy–momentum tensor in this context and obtain the vacuum solution of MMS and its weak field limit in the spherically symmetric coordinates. We show that while it is already a vacuum solution, it can simulate dark matter when restricted to the framework of general relativity, i.e., a symmetry-broken conformal frame. This is done by employing a density function which is an essential part of MMS. We derive an equation for the density function for a general profile of a rotation curve obtained from observations. Specifically, the density function corresponding to two well-known profiles PSS and NFW are provided.

Topological effects on non-relativistic eigenvalue solutions under AB-flux field with pseudoharmonic- and Mie-type potentials

In this paper, we investigate the quantum dynamics of a non-relativistic particle confined by the Aharonov–Bohm quantum flux field with pseudoharmonic-type potential in the background of topological defect produced by a point-like global monopole. We solve the radial Schrödinger equation analytically and determine the exact eigenvalue solution of the quantum system. Afterwards, we consider a Mie-type potential in the quantum system and solve the radial equation analytically and obtain the eigenvalue solution. We analyze the effects of the topological defect and the quantum flux with these potentials on the energy eigenvalue and wave function of the non-relativistic particles. In fact, it is shown that the energy levels and wave functions are influenced by the topological defect shifted the result compared to the flat space results. In addition, the quantum flux field also shifted the eigenvalue solutions and an analogue of the Aharonov–Bohm effect for bound-states is observed. Finally, we utilize these eigenvalue solutions to some known diatomic molecular potential models and presented the energy eigenvalue and wave function.

CERTAIN COSMOLOGICAL MODELS WITH VARIATION OF HUBBLE PARAMETER

The present paper deals with the FRW-Cosmological Model of universe for W2 flat perfect fluid space time. Einstein field equations with variable cosmological constant (Λ) has been obtained for such spacetime and in order to get the complete cosmological solution the law of variation for Hubble’s parameter is considered. A new class of solution have been discussed for the Einstein field equations with variable cosmological constant in which the pressure, energy density, and cosmological constant Λ are found to be decreasing function of cosmic time. The physical and kinematical properties of models are also discussed.

Higher-spin Yang–Mills, amplitudes and self-duality

The existence of interacting higher-spin theories is tightly constrained by many no-go theorems. In this paper, we construct a chiral, higher-spin generalization of Yang–Mills theory in flat space which avoids these no-go theorems and has non-trivial tree-level scattering amplitudes with some higher-spin external legs. The fields and action are complex, so the theory is non-unitary and parity-violating, yet we find surprisingly compact formulae for all-multiplicity tree-level scattering amplitudes in the maximal helicity violating (MHV) sector, where the two negative helicity particles have identical but arbitrary spin. This is possible because the theory admits a perturbative expansion around its self-dual sector. Using twistor theory, we prove the classical integrability of this self-dual sector and show that it can be described on spacetime by an infinite tower of interacting massless scalar fields. We also give a twistor construction of the full theory and use it to derive the formula for the MHV amplitude.

AdS Witten diagrams to Carrollian correlators

Carrollian Conformal Field Theories (CFTs) have been proposed as co-dimension one holographic duals to asymptotically flat spacetimes as opposed to Celestial CFTs which are co-dimension two. In this paper, drawing inspiration from Celestial holography, we show by a suitable generalisation of the flat space limit of AdS that keeps track of the previously disregarded null direction, one can reproduce Carrollian CFT correlation functions from AdS Witten diagrams. In particular, considering Witten diagrams in AdS4, we reproduce two and three-point correlation functions for three dimensional Carrollian CFTs in the so-called delta-function branch. Along the way, we construct non-trivial Carrollian three-point functions in the delta-branch by considering a collinear limit. We also obtain a generalised anti-podal matching condition that now depends on the retarded time direction.

Local continuity of angular momentum and noether charge for matter in general relativity

Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate of change of energy-momentum within a finite spacelike volume is equivalent to the flux integrated over the surface of this volume; for general spacetimes it is necessary to include a volume integral of a source term arising from spacetime curvature. In this work a study of continuity of matter in general relativity is extended to include angular momentum of matter and Noether currents associated with gauge symmetries. Expressions for the Noether charge and flux of complex scalar fields and complex Proca fields are found using this formalism. Expressions for the angular momentum density, flux and source are also derived which are then applied to a numerical relativity collision of boson stars in 3D with non-zero impact parameter as an illustration of the methods.

Influencing Factors on Changes in the Unified Exterior Form Facing the Street

A unified original townscape may affect the identity and value of the area. However, it is not easy to maintain the original design as time passes. This study aims to clarify the actual remaining state of exterior form within suburban detached residential areas and explore the influencing factors. For data collection, visual observation of the site and a literature survey on the housing map was conducted. For analysis, we conducted the cross-tabulation, chi-square test, and association analysis. The following results are obtained: 1) In about 80% of the lots, both planting belts and hedges are maintained after 23-37 years of development. The hedge is more likely to disappear than the planting belts, 2) Rebuilding, household alternation, and multiple flat parking spaces are three significant factors influencing the disappearance of planting belts and hedges. The impact of rebuilding is the predominant factor in the disappearance of both. Furthermore, the impact of rebuilding is strengthened when combined with household alternation or multiple flat parking spaces, and 3) The relationship between the remaining exterior features and duration after development by the areas and joining communal building agreements was not confirmed.

Gravitational Decoupling as a Generator of Curvature and Matter Distribution

AbstractIn this work, we generate curved Lorentzian manifolds from a flat Minkowskian space–time, through the Gravitational Decoupling by the Minimal Geometric Deformation method interpreting the decoupling sector as a generator of curvature and matter distribution. In particular, we obtain some new wormhole geometries by imposing either physically relevant equations of state or certain physically–motivated geometric constraints. These solutions are analyzed in detail. For all these solutions, we study the associated energy conditions, the geometric behavior and construct their embedding diagrams.

4D flat-space scattering amplitude/CFT3 correlator correspondence revisited

In this paper, we make connection between CFT3 three point correlation function of conserved currents and 4D three point amplitude of general spin massless gauge field explicit. We do so by taking flat space limit of momentum space CFT correlation function and show how they reproduce flat space amplitudes. We then point out a mismatch between number of independent structures in 3D CFT correlator of conserved currents and 4D flat space covariant vertex of massless higher spin fields. This is in contrast with general expectation that counting of 3d CFT correlator and 4d flat space amplitude should match. This mismatch is even more pronounced in spinor helicity variables.We also point out an interesting relation between parity even and parity odd flat space amplitude in momentum space. This observation helps us to construct a new momentum space CFT structure which accounts for the mismatch. However we should mention that this extra CFT structure can't be constructed out of conserved currents and hence counting mismatch between CFT correlation of conserved currents and flat space amplitude of massless gauge field persists. Story in spinor helicity variable is more complicated and is discussed in detail. We further comment on the connection of CFT correlation function in spinor helicity variables to AdS amplitudes in spinor helicity variables and light cone variables.

Bern-Carrasco-Johansson relations in AdS5×S3 and the double-trace spectrum of super gluons

We revisit the four-point function of super gluons in $AdS_5 \times S^3$ in the spirit of the large $p$ formalism and show how the integrand of a generalised Mellin transform satisfies various non-trivial properties such as $U(1)$ decoupling identity, BCJ relations and colour-kinematic duality, in a way that directly mirrors the analogous relations in flat space. We unmix the spectrum of double-trace operators at large $N$ and find all anomalous dimensions at leading order. The anomalous dimensions follow a very simple pattern, resembling those of other theories with hidden conformal symmetries.

Anomaly-free scale symmetry and gravity

In this Letter, we address the question of whether the conformal invariance can be considered as a global symmetry of a theory of fundamental interactions. To describe Nature, this theory must contain a mechanism of spontaneous breaking of the scale symmetry. Besides that, the fundamental theory must include gravity, whereas all known extensions of the conformal invariance to the curved space-time suffer from the Weyl anomaly. We show that conformal symmetry can be made free from quantum anomaly only in flat space. The presence of gravity would reduce the global symmetry group of the fundamental theory to the scale invariance only. We discuss how the effective Lagrangian respecting the scale symmetry can be used for the description of particle phenomenology and cosmology.

Gravitational collapse and odd-parity black hole perturbations in minimal theory of bigravity

In the former part, we study the gravitational collapse of pressureless dust and find special solutions, where, in both the physical and fiducial sectors, the exterior and interior spacetime geometries are given by the Schwarzschild spacetimes and the Friedmann-Lema\^itre-Robertson-Walker universes dominated by pressureless dust, respectively, with specific time slicings. In the case where the Lagrange multipliers are trivial and have no jump across the matter interfaces in both the physical and fiducial sectors, the junction conditions across them remain the same as those in general relativity (GR). For simplicity, we foliate the interior geometry by homogeneous and isotropic spacetimes. For a spatially flat interior universe, we foliate the exterior geometry by a time-independent flat space, while for a spatiallycurved interior universe, we foliate the exterior geometry by a time-independent space with deficit solid angle. Despite the rather restrictive choice of foliations, we find interesting classes of exact solutions that represent gravitational collapse in MTBG. In the spatially flat case, under a certain tuning of the initial condition, we find exact solutions of matter collapse in which the two sectors evolve independently. In the spatially closed case, once the matter energy densities and the Schwarzschild radii are tuned between the two sectors, we find exact solutions that correspond to the Oppenheimer-Snyder model in GR. In the latter part, we study odd-parity perturbations of the Schwarzschild$-$de Sitter solutions written in the spatially flat coordinates. For the higher-multipole modes $\ell\geq2$, we find that, in general, the system reduces to that of four physical modes, where two of them are dynamical and the remaining two are shadowy, i.e., satisfying only elliptic equations.

Graviton scattering in self-dual radiative space-times

The construction of amplitudes on curved space-times is a major challenge, particularly when the background has non-constant curvature. We give formulae for all tree-level graviton scattering amplitudes in curved self-dual (SD) radiative space-times; these are chiral, source-free, asymptotically flat spaces determined by free characteristic data at null infinity. Such space-times admit an elegant description in terms of twistor theory, which provides the powerful tools required to exploit their underlying integrability. The tree-level S-matrix is written in terms of an integral over the moduli space of holomorphic maps from the Riemann sphere to twistor space, with the degree of the map corresponding to the helicity configuration of the external gravitons. For the MHV sector, we derive the amplitude directly from the Einstein–Hilbert action of general relativity, while other helicity configurations arise from a natural family of generating functionals and pass several consistency checks. The amplitudes in SD radiative space-times exhibit many novel features that are absent in Minkowski space, including tail effects. There remain residual integrals due to the functional degrees of freedom in the background space-time, but our formulae have many fewer such integrals than would be expected from space-time perturbation theory. In highly symmetric special cases, such as SD plane waves, the number of residual integrals can be further reduced, resulting in much simpler expressions for the scattering amplitudes.

Field Mixing in Curved Spacetime and Dark Matter

An extensive review of recent results concerning the quantum field theory of particle mixing in curved spacetime is presented. The rich mathematical structure of the theory for both fermions and bosons, stemming from the interplay of curved space quantization and field mixing, is discussed, and its phenomenological implications are shown. Fermionic and bosonic oscillation formulae for arbitrary globally hyperbolic spacetimes are derived and the transition probabilities are explicitly computed on some metrics of cosmological and astrophysical interest. The formulae thus obtained are characterized by a pure QFT correction to the amplitudes, which is absent in quantum mechanics, where only the phase of the oscillations is affected by the gravitational background. Their deviation from the flat space probabilities is demonstrated, with the aid of numerical analyses. The condensate structure of the flavor vacuum of mixed fermions is studied, assessing its role as a possible dark matter component in a cosmological context. It is shown that the flavor vacuum behaves as a barotropic fluid, satisfying the equation of the state of cold dark matter. New experiments on the cosmic neutrino background, as PTOLEMY, may validate these theoretical results.