Minkowski Space Research Articles

Radiation in holography

We show how to encode the radiative degrees of freedom in 4-dimensional asymptotically AdS spacetimes, using the boundary Cotton and stress tensors. Background radiation leads to a reduction of the asymptotic symmetry group, in contrast to asymptotically flat spacetimes, where a non-vanishing news tensor does not restrict the asymptotic symmetries. Null gauges, such as Λ-BMS, provide a framework for AdS spacetimes that include radiation in the flat limit. We use this to check that the flat limit of the radiative data matches the expected definition in intrinsically asymptotically flat spacetimes. We further dimensionally reduce our construction to the celestial sphere, and show how the 2-dimensional celestial currents can be extracted from the 3-dimensional boundary data.

Thermodynamic relation of accelerating black holes in anti-de Sitter spacetime

We consider accelerating black holes in four-dimensional anti-de Sitter spacetime and investigate the extremality relations by examining perturbative corrections to both the entropy of black holes and their extremality bounds. It is shown that the so-called Goon and Penco (univeral) relation is also valid for accelerating black holes. Furthermore, it is found that an appropriate matching condition is necessary between the perturbation parameter of the relation with the perturbative correction to such black holes, and the parameter with information about the conical deficits on the north and south poles with the cosmic string tensions in order to satisfy the extremality relations. This result indicates that the extremality (univeral) relation of a class of accelerating black holes holds exhibit behavior similar to the Weak Gravity Conjecture.

The distribution amplitude of the ηc-meson at leading twist from lattice QCD

Distribution amplitudes are functions of non-perturbative matrix elements describing the hadronization of quarks and gluons. Thanks to factorization theorems, they can be used to compute the scattering amplitude of high-energy processes. Recently, new ideas have allowed their computation using lattice QCD, which should provide us with a general, fully relativistic determination. We present the first lattice calculation of the ηc-meson distribution amplitude at leading twist. Starting from the relevant matrix element in discrete Euclidean space on a set of Nf = 2 CLS ensembles, we explain the method to connect to continuum Minkowski spacetime. After addressing several sources of systematic uncertainty, we compare to Dyson-Schwinger and non-relativistic QCD determinations of this quantity. We find significant deviations between the latter and our result even at small Ioffe times.

Holographic reconstruction of flat spacetime

The flat/CFT dictionary between the bulk gravitational theory and boundary conformal field theory is systematically developed in this paper. Asymptotically flat spacetime is built up by asymptotically AdS hyperboloid slices in terms of Fefferman Graham coordinates together with soft modes propagating between different slices near the null boundary. Then we construct the flat holography dictionary based on studying the Einstein equation at zero and first order and it turns out that these correspond to the description of hard and soft sector for the field theory from the boundary point of view. The explicit expression for energy-stress tensor is also determined by performing holographic renormalisation on the Einstein Hilbert action. By studying the anomalies of the energy-stress tensor, we obtain the leading and subleading contribution to the central charge. Einstein equations in the bulk are related to the Ward identities of the boundary theory and we find that the boundary CFT energy-stress tensor is not conserved due to the existence of radiative soft modes which will generate the energy flow through the null boundary.

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The Yang–Mills–Chern–Simons theory in three-dimensional Minkowski space-time is studied in a gauge-fixing scheme which interpolates between the covariant gauge and light-cone gauge, the interpolating gauge-fixing. The ultraviolet finiteness of the theory is proved via the Becchi–Rouet–Stora (BRS) algebraic renormalization procedure, which allows us to demonstrate the vanishing of all β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-functions and all anomalous dimensions to all orders in perturbation theory.

Modes of the Sakai-Sugimoto soliton

Abstract The instanton in the Sakai-Sugimoto model corresponds to the Skyrmion on the holographic boundary - which is asymptotically flat - and is fundamentally different from the flat Minkowski space Yang-Mills instanton. We use the Atiyah-Patodi-Singer index theorem and a series of transformations to show that there are 6k zeromodes - or moduli - in the limit of infinite 't Hooft coupling of the Sakai-Sugimoto model. The implications for the low-energy baryons - the Skyrmions - on the holographic boundary, is a scale separation between 2k "heavy" massive modes and 6k-9 "light" massive modes for k>1; the 9 global transformations that correspond to translations, rotations and isorotations remain as zeromodes. For k=1 there are 2 "heavy" modes and 6 zeromodes due to degeneracy between rotations and isorotations.

Nambu-Goto equation from three-dimensional gravity

We demonstrate that the solutions of three-dimensional gravity obtained by gluing two copies of a spacetime across a junction constituted of a tensile string are in one-to-one correspondence with the solutions of the Nambu-Goto equation in the same spacetime up to a finite number of rigid deformations related to worldsheet and spacetime isometries. The non-linear Nambu-Goto equation satisfied by the average of the embedding coordinates of the junction emerges directly from the junction conditions along with the rigid deformations and corrections due to the tension. Therefore, the equivalence principle generalizes non-trivially to the string. Our results are valid both in three-dimensional flat and AdS spacetimes. In the context of AdS3/CFT2 correspondence, our setup could be used to describe a class of interfaces in the conformal field theory featuring relative time reparametrization at the interface which encodes the solution of the Nambu-Goto equation corresponding to the bulk junction.

Special Relativity, Mass, and Energy; E=mc2

The purpose of this paper to provide a proof of  using a derivation completely consistent with Special Relativity. We base our proof on the calculation of the relativistic kinetic energy, K, and the invariance of the momentum 4-vector in Minkowski space. This proof provides a useful pedagogical method for teaching the momentum 4-vector through an excellent example to undergraduate physics students.

Inclusive reactions from finite Minkowski spacetime correlation functions

The need to determine scattering amplitudes of few-hadron systems for arbitrary kinematics expands a broad set of subfields of modern-day nuclear and hadronic physics. In this work, we expand upon previous explorations on the use of real-time methods, like quantum computing or tensor networks, to determine few-body scattering amplitudes. Such calculations must be performed in a finite Minkowski spacetime, where scattering amplitudes are not well defined. Our previous work presented a conjecture of a systematically improvable estimator for scattering amplitudes constructed from finite-volume correlation functions. Here we provide further evidence that the prescription works for larger kinematic regions than previously explored as well as a broader class of scattering amplitudes. Finally, we devise a new method for estimating the order of magnitude of the error associated with finite time separations needed for such calculations. In units of the lightest mass of the theory, we find that to constrain amplitudes using real-time methods within O(10%), the spacetime volumes must satisfy mL∼O(10–102)) and mT∼O(102–104). Published by the American Physical Society 2024

Two-Dimensional Nonisotropic Surfaces with Flat Normal Connection and a Nondegenerate Grassmann Image of Constant Curvature in the Minkowski Space

Two-Dimensional Nonisotropic Surfaces with Flat Normal Connection and a Nondegenerate Grassmann Image of Constant Curvature in the Minkowski Space

The 4-Dimensional Spacetime World Line Image Representation and the Law of Existence of Objects Inferred from it

MINKOWSKI defined the four-dimensional spacetime model (x, y, z, t) used to represent world-point and world in [1]. The spacetime light cone is an intuitive diagram, compacted one space component and replaced it by time axis, thus the spacetime light cone was based on (x, y, t). In such a way, although it made the visual expression is possible, but also the spacetime light cone exposed shortages as follows • The spacetime light cone has limited expressive ability • The relationship between two or more world lines or events cannot be expressed • Can't express different world lines correctly • Most images of spacetime light cones are wrong and no use • The image of spacetime light cone is not intuitive and is obscure in application. Because of this, we designed the 4-dimensional Spacetime World Line image representation. This new 4-dimensional Spacetime diagram presents the complete 3 space dimensions and 1 time dimension. It overcomes the weakness of spacetime light cone, gives clear and precise visual expression of the world line, is able to display multi-world lines in one figure, can clearly present the interface and development process of each of the world line, and display the interaction among them. From the 4-dimensional spacetime diagram, we deducted and proved the Law of Existence of Object, which is as such: From its birth, through its past, to the present, and into the future, an object only exists at the "present" moment.

An effective model for the quantum Schwarzschild black hole: Weak deflection angle, quasinormal modes and bounding of greybody factor

In this paper, we thoroughly explore two crucial aspects of a quantum Schwarzschild black solution within four-dimensional space–time: (i) the weak deflection angle, (ii) the rigorous greybody factor and, (iii) the Dirac quasinormal modes. Our investigation involves employing the Gauss–Bonnet theorem to precisely compute the deflection angle and establishing its correlation with the Einstein ring. Additionally, we derive the rigorous bounds for greybody factors through the utilization of general bounds for reflection and transmission coefficients in the context of Schrodinger-like one-dimensional potential scattering. We also compute the corresponding Dirac quasinormal modes using the WKB approximation. We reduce the Dirac equation to a Schrodinger-like differential equation and solve it with appropriate boundary conditions to obtain the quasinormal frequencies. To visually underscore the quantum effect, we present figures that illustrate the impact of varying the parameter r0, or more specifically, in terms of the parameter α. This comprehensive examination enhances our understanding of the quantum characteristics inherent in the Schwarzschild black solution, shedding light on both the deflection angle and greybody factors in a four-dimensional space–time framework.

Retrieving Yang–Mills–Higgs fields in Minkowski space from active local measurements

Retrieving Yang–Mills–Higgs fields in Minkowski space from active local measurements

Relativistic generalized uncertainty principle for a test particle in four-dimensional spacetime

The generalized uncertainty principle provides a promising phenomenological approach to reconciling the fundamentals of general relativity with quantum mechanics. As a result, noncommutativity, measurement uncertainty, and the fundamental theory of quantum mechanics are subject to finite gravitational fields. The generalized uncertainty principle (RGUP) on curved spacetime allows for the imposition of quantum-induced elements on general relativity (GR) in four dimensions. In the relativistic regimes, the determination of a test particle’s spacetime coordinates, [Formula: see text], becomes uncertain. There exists a specific range of coordinates where the accessibility to [Formula: see text] is notably limited. Consequently, the spacetime coordinates lack both smoothness and continuity. The quantum-mechanical calculations of the spacetime coordinates are directly linked to their measurement through the expectation value [Formula: see text]. This expectation value is dependent on [Formula: see text], which is itself limited by a minimum measurable length [Formula: see text]. A crucial finding presented in this script is the existence of a lower bound for the Hamiltonian, which implies the stability of the quantum nature of spacetime. The direct correlation between [Formula: see text] and [Formula: see text] is a significant discovery, suggesting a proportional relationship. The conjecture is made that the primary metric g carries all essential information regarding spacetime curvature and serves a role akin to the Jacobian determinant in general relativity. Moreover, the linear relationship between [Formula: see text] and the Planck length [Formula: see text] is established with a proportionality factor of [Formula: see text], where [Formula: see text] denotes the RGUP parameter. The discretization of spacetime coordinates results in the discontinuity of the test particle’s wavefunction [Formula: see text], leading to an unrealistic [Formula: see text]. It is also noted that the lower limit of [Formula: see text] is directly proportional to the fundamental tensor.

Uniqueness of the static vacuum asymptotically flat spacetimes with massive particle spheres

In this paper, we establish that a four-dimensional static vacuum asymptotically flat spacetime containing a massive particle sphere is isometric to the Schwarzschild spacetime. Our results expand upon existing uniqueness theorems for static vacuum asymptotically flat spacetimes, which focus on scenarios featuring event horizons or photon spheres. Similarly to the uniqueness theorems concerning photon spheres or event horizons, only a single massive particle sphere is sufficient to obtain a unique solution. However, in contrast to previous theorems, our result leads to the existence of an entire spacetime foliation sliced by a set of massive particle spheres spanning various energies. Published by the American Physical Society 2024

A de Sitter S-matrix from amputated cosmological correlators

Extending scattering to states with unphysical mass values (particles “off their mass shell”) has been instrumental in developing modern amplitude technology for Minkowski spacetime. Here, we study the off-shell correlators which underpin the recently proposed S-matrix for scattering on de Sitter spacetime. By labelling each particle with both a spatial momentum and an independent “energy” variable (the de Sitter analogue of a 4-momentum), we find that the practical computation of these correlators is greatly simplified. This allows us to derive compact expressions for all 3- and 4-particle S-matrices at tree-level for scalar fields coupled through any derivative interactions. As on Minkowski, we find that the 3-particle and exchange part of the 4-particle S-matrices are unique (up to crossing). The remaining contact part of the 4-particle S-matrix is an analytic function of just two differential operators, which become the usual Mandelstam variables in the Minkowski limit. Finally, we introduce a spectral decomposition for the tree-level exchange of a heavy field responsible for a cosmological collider signal. Once projected onto physical mass eigenstates, these S-matrix elements encode the statistical properties of the early inflationary perturbations.

General mass formulas for charged Kerr-AdS black holes

It is well-known that the mass of a non-asymptotically flat spacetime cannot be uniquely defined. Some mass formulas for the Kerr-AdS black hole have been found and used in studying black hole thermodynamics. However, the derivations usually need a background subtraction to eliminate the divergence at infinity. It is also unknown whether the mass depends on the choice of coordinates. In this paper, we provide a more straightforward derivation for the mass formula, only demanding that the first law of black hole thermodynamics and Smarr formula are satisfied. We first make use of the Iyer-Wald formalism to derive a first law which avoids the divergence at infinity. Then we apply this formula to charged Kerr-AdS black hole expressed in the coordinates rotating at infinity. However, the first law associated with the timelike Killing vector field ∂∂t is not integrable. Then, by making use of the gauge freedom of t, we find a favorite parameter t′ which just makes the mass integrable. Applying the scaling argument, we show that the mass satisfies the Smarr formula and takes the form M/Ξ3/2. Moreover, applying the conformal method with ∂∂t′ , we obtain the same mass. By applying the first law to the coordinates which is not rotating at infinity, we find a preferred time T that makes the first law integrable and the mass is just the familiar mass M/Ξ2 in the literature. This mass is also confirmed by the conformal method. We find that the two mass formulas correspond to different families of observers and the preferred Killing times. So our work clarifies the ambiguities of mass in Kerr-AdS spacetimes.

Tessellation and interactive visualization of four-dimensional spacetime geometries

This paper addresses two problems needed to support four-dimensional (3d+t) spacetime numerical simulations. The first contribution is a general algorithm for producing conforming spacetime meshes of moving geometries. Here, the surface points of the geometry are embedded in a four-dimensional space as the geometry moves in time. The geometry is first tessellated at prescribed time steps and then these tessellations are connected in the parameter space of each geometry entity to form tetrahedra. In contrast to previous work, this approach allows the resolution of the geometry to be controlled at each time step. The only restriction on the algorithm is the requirement that no topological changes to the geometry are made (i.e. the hierarchical relations between all geometry entities are maintained) as the geometry moves in time. The validity of the final mesh topology is verified by ensuring the tetrahedralizations represent a closed 3-manifold. For some analytic problems, the 4d volume of the tetrahedralization is also verified. The second problem addressed in this paper is the design of a system to interactively visualize four-dimensional meshes when the 4d view changes, including tetrahedra (embedded in 4d) and pentatopes. Algorithms that either include or exclude a geometry shader are described, and the efficiency of each approach is then compared. Overall, the results suggest that visualizing tetrahedra (either those bounding the domain, or extracted from a pentatopal mesh) using a geometry shader achieves the highest frame rate, realizing interactive frame rates of at least 15 frames per second for meshes with about 50 million tetrahedra.

Quantum charged black holes

Within the framework of braneworld holography, we construct a quantum charged black hole localized on a three-dimensional anti-de Sitter (AdS) brane that intersects the asymptotic boundary of the four-dimensional AdS spacetime at the conformal defects and incorporates quantum backreaction effects from the conformal field theory (CFT) on the brane. This quantum charged black hole is an exact solution of the semiclassical gravitational equation corresponding to a theory with higher curvature gravity and nonminimally coupled nonlinear gauge field. In the framework of double holography, we investigate the thermodynamics of the quantum charged black hole from three perspectives: a pure bulk perspective, in which four-dimensional classical Einstein gravity couples to Maxwell electrodynamics and a codimension-one tensional brane; a brane perspective, where semiclassical higher curvature gravity is subject to quantum backreaction from the holographic CFT on the brane, yielding a quantum charged black hole; and a boundary perspective, where the defect CFT is coupled to a boundary CFT at the asymptotic boundary and the degrees of freedom for defect quantum conformal matter is considered. In so doing, we obtain doubly holographic formulations of both the first law of thermodynamics and the Smarr (energy) relations for the quantum charged black holes.

Asymptotic symmetries from the string worldsheet

In IIB string theory on AdS3 background with NS-NS fluxes, we show that Brown-Henneaux asymptotic Killing vectors can be derived by requiring both the worldsheet equations of motion and Virasoro constraints are preserved near the asymptotic boundary of the target spacetime. The charges on the worldsheet that generate the corresponding transformations can be written down in both the Lagrangian formalism and Hamiltonian formalism. This provides a method of studying asymptotic symmetry of the target spacetime directly from worldsheet string theories, without using results from the supergravity limit. As an example, we apply this method to flat spacetime in three dimensions and obtain the BMS3 generators on the worldsheet theory.