Spacetime Dimensions Research Articles

Infrared finite scattering theory: Amplitudes and soft theorems

Any nontrivial scattering with massless fields in four spacetime dimensions will generically produce an out-state with memory. Scattering with any massless fields violates the standard assumption of asymptotic completeness—that all “in” and “out” states lie in the standard (zero-memory) Fock space—and therefore leads to infrared divergences in the standard S-matrix amplitudes. In this paper, we define an infrared finite scattering theory which assumes only (1) the existence of in-/out-algebras and (2) that Heisenberg evolution is an automorphism of these algebras. The resulting “superscattering” map $ allows for transitions between different in/out memory states and agrees with the standard S matrix when it is defined. We construct $ amplitudes by defining (3) a “generalized asymptotic completeness” which accommodates states with memory in the space of asymptotic states and (4) a complete basis of improper states that generalize the usual n-particle momentum basis to account for states with memory. Using only general properties of $, we prove an analog of the Weinberg soft theorems in quantum gravity and QED which imply that all $ amplitudes are well defined in the infrared. We comment on how one must generalize this framework to consider $ amplitudes for theories with collinear divergences (e.g., massless QED and Yang-Mills theories). Published by the American Physical Society 2024

Relational Lorentzian Asymptotically Safe Quantum Gravity: Showcase Model

In a recent contribution, we identified possible points of contact between the asymptotically safe and canonical approaches to quantum gravity. The idea is to start from the reduced phase space (often called relational) formulation of canonical quantum gravity, which provides a reduced (or physical) Hamiltonian for the true (observable) degrees of freedom. The resulting reduced phase space is then canonically quantized, and one can construct the generating functional of time-ordered Wightman (i.e., Feynman) or Schwinger distributions, respectively, from the corresponding time-translation unitary group or contraction semigroup, respectively, as a path integral. For the unitary choice, that path integral can be rewritten in terms of the Lorentzian Einstein–Hilbert action plus observable matter action and a ghost action. The ghost action depends on the Hilbert space representation chosen for the canonical quantization and a reduction term that encodes the reduction of the full phase space to the phase space of observables. This path integral can then be treated with the methods of asymptotically safe quantum gravity in its Lorentzian version. We also exemplified the procedure using a concrete, minimalistic example, namely Einstein–Klein–Gordon theory, with as many neutral and massless scalar fields as there are spacetime dimensions. However, no explicit calculations were performed. In this paper, we fill in the missing steps. Particular care is needed due to the necessary switch to Lorentzian signature, which has a strong impact on the convergence of “heat” kernel time integrals in the heat kernel expansion of the trace involved in the Wetterich equation and which requires different cut-off functions than in the Euclidian version. As usual we truncate at relatively low order and derive and solve the resulting flow equations in that approximation.

Spherical accretion onto higher-dimensional Reissner–Nordström black hole

Abstract We obtain relativistic solutions of spherically symmetric accretion by a dynamical analysis of a generalised Hamiltonian for higher-dimensional Reissner–Nordström (RN) Black Hole (BH). We consider two different fluids namely, an isotropic fluid and a non-linear polytropic fluid to analyse the critical points in a higher-dimensional RN BH. The flow dynamics of the fluids are studied in different spacetime dimensions in the framework of Hamiltonian formalism. The isotropic fluid is found to have both transonic and non-transonic flow behaviour, but in the case of polytropic fluid, the flow behaviour is found to exhibit only non-transonic flow, determined by a critical point that is related to the local sound speed. The critical radius is found to change with the spacetime dimensions. Starting from the usual four dimensions it is noted that as the dimension increases the critical radius decreases, attains a minimum at a specific dimension (D > 4) and thereafter increases again. The mass accretion rate for isotropic fluid is determined using Hamiltonian formalism. The maximum mass accretion rate for RN BH with different equations of state parameters is studied in addition to spacetime dimensions. The flow behaviour and mass accretion rate for a change in BH charge is also studied analytically. It is noted that the maximum mass accretion rate in a higher-dimensional Schwarzschild BH is the lowest, which however, increases with the increase in charge parameter in a higher-dimensional RN BH.

Bounds on photon scattering

We study 2-to-2 scattering amplitudes of massless spin one particles in d = 4 space-time dimensions, like real world photons. We define a set of non-perturbative observables (Wilson coefficients) which describe these amplitudes at low energies. We use full non-linear unitarity to construct various novel numerical bounds on these observables. For completeness, we also rederive some bounds using positivity only. We discover and explain why some of these Wilson coefficients cannot be bounded.

Higher spins and Finsler geometry

Finsler geometry is a natural generalization of (pseudo-)Riemannian geometry, where the line element is not the square root of a quadratic form but a more general homogeneous function. Parameterizing this in terms of symmetric tensors suggests a possible interpretation in terms of higher-spin fields. We will see here that, at linear level in these fields, the Finsler version of the Ricci tensor leads to the curved-space Fronsdal equation for all spins, plus a Stueckelberg-like coupling. Nonlinear terms can also be systematically analyzed, suggesting a possible interacting structure. No particular choice of spacetime dimension is needed. The Stueckelberg mechanism breaks gauge transformations to a redundancy that does not change the geometry. This creates a serious issue: non-transverse modes are not eliminated, at least for the versions of Finsler dynamics examined in this paper.

Quantum scalar field on fuzzy de Sitter space. Part I. Field modes and vacua

We study a scalar field on a noncommutative model of spacetime, the fuzzy de Sitter space, which is based on the algebra of the de Sitter group SO(1, d) and its unitary irreducible representations. We solve the Klein-Gordon equation in d = 2, 4 and show, using a specific choice of coordinates and operator ordering, that all commutative field modes can be promoted to solutions of the fuzzy Klein-Gordon equation. To explore completeness of this set of modes, we specify a Hilbert space representation and study the matrix elements (integral kernels) of a scalar field: in this way the complete set of solutions of the fuzzy Klein-Gordon equation is found. The space of noncommutative solutions has more degrees of freedom than the commutative one, whenever spacetime dimension is d > 2. In four dimensions, the new non-geometric, internal modes are parametrised by S2 × W, where W is a discrete matrix space. Our results pave the way to analysis of quantum field theory on the fuzzy de Sitter space.

Lie symmetries in higher dimensional charged radiating stars

This study investigates the Lie symmetry properties of matter variables, spacetime dimension, and kinematic quantities in spherically symmetric radiating stars undergoing gravitational collapse in higher dimensional spacetimes. Our analysis explores how variations in functions and dependent variables influence the Lie algebra dimensionality and Lie symmetries of the boundary condition. Our study reveals the explicit dependence of charge and spacetime dimension in the Lie symmetry generators for the first time. We examine models with various kinematical features, such as shear, shear-free, geodesic, and non-expanding conditions with different matter variables. Using the Lie symmetries we obtain group invariant solutions to the models and observe how the kinematical features and matter variables affect the Lie symmetries. Additionally, we demonstrate the appearance of a linear equation of state. We recover known four-dimensional models from our results.

Piecewise linear potentials for false vacuum decay and negative modes

We study bounce solutions and associated negative modes in the class of piecewise linear triangular-shaped potentials that may be viewed as approximations of smooth potentials. In these simple potentials, the bounce solution and action can be obtained analytically for a general spacetime dimension D. The eigenequations for the fluctuations around the bounce are universal and have the form of a Schrödinger-like equation with delta-function potentials. This Schrödinger equation is solved exactly for the negative modes whose number is confirmed to be one. The latter result may justify the usefulness of such piecewise linear potentials in the study of false vacuum decay. Published by the American Physical Society 2024

Metrics depending on one variable in D -dimensional Einstein-Maxwell theory

We present new families of solutions of D-dimensional Einstein-Maxwell theory depending on one variable for all space-time signatures. The solutions found can be thought of as generalized Melvin solutions including flux tubes, domain walls, and cosmological space-times. Explicit examples are given in four and five space-time dimensions. Published by the American Physical Society 2024

The Asymptotic Expansion of the Spacetime Metric at the Event Horizon

AbstractHawking’s local rigidity theorem, proven in the smooth setting by Alexakis-Ionescu-Klainerman, says that the event horizon of any stationary non-extremal black hole is a non-degenerate Killing horizon. In this paper, we prove that the full asymptotic expansion of any smooth vacuum metric at a non-degenerate Killing horizon is determined by the geometry of the horizon. This gives a new perspective on the black hole uniqueness conjecture. In spacetime dimension 4, we also prove an existence theorem: Given any non-degenerate horizon geometry, Einstein’s vacuum equations can be solved to infinite order at the horizon in a unique way (up to isometry). The latter is a gauge invariant version of Moncrief’s classical existence result, without any restriction on the topology of the horizon. In the real analytic setting, the asymptotic expansion is shown to converge and we get well-posedness of this characteristic Cauchy problem.

Ftint: Calculating gradient-flow integrals with pySecDec

The program ftint is introduced which numerically evaluates dimensionally regularized integrals as they occur in the perturbative approach to the gradient-flow formalism in quantum field theory. It relies on sector decomposition in order to determine the coefficients of the individual orders in ϵ=(4−D)/2, where D is the space-time dimension. For that purpose, it implements an interface to the public library pySecDec. The current version works for massive and massless integrals up to three-loop level with vanishing external momenta, but the underlying method is extendable to more general cases.

Gluonic evanescent operators: negative-norm states and complex anomalous dimensions

In this paper, we build on our previous work to further investigate the role of evanescent operators in gauge theories, with a particular focus on their contribution to violations of unitarity. We develop an efficient method for calculating the norms of gauge-invariant operators in Yang-Mills (YM) theory by employing on-shell form factors. Our analysis, applicable to general spacetime dimensions, reveals the existence of negative-norm states among evanescent operators. We also explore the one-loop anomalous dimensions of these operators and find complex anomalous dimensions. We broaden our analysis by considering YM theory coupled with scalar fields and we observe similar patterns of non-unitarity. The presence of negative-norm states and complex anomalous dimensions across these analyses provides compelling evidence that general gauge theories are non-unitary in non-integer spacetime dimensions.

Numerical conformal bootstrap with analytic functionals and outer approximation

This paper explores the numerical conformal bootstrap in general spacetime dimensions through the lens of a distinct category of analytic functionals, previously employed in two-dimensional studies. We extend the application of these functionals to a more comprehensive backdrop, demonstrating their adaptability and efficacy in general spacetime dimensions above two. The bootstrap is implemented using the outer approximation methodology, with computations conducted in double precision. The crux of our study lies in comparing the performance of this category of analytic functionals with conventional derivatives at crossing symmetric points. It is worth highlighting that in our study, we identified some novel kinks in the scalar channel during the maximization of the gap in two-dimensional conformal field theory. Our numerical analysis indicates that these analytic functionals offer a superior performance, thereby revealing a potential alternative paradigm in the application of conformal bootstrap.

Generalization of conformal Hamada operators

AbstractThe six-derivative conformal scalar operator was originally found by Hamada in its critical dimension of spacetime, $$d=6$$ d = 6 . We generalize this construction to arbitrary dimensions d by adding new terms cubic in gravitational curvatures and by changing its coefficients of expansion in various curvature terms. The consequences of global scale-invariance and of infinitesimal local conformal transformations are derived for the form of this generalized operator. The system of linear equations for coefficients is solved giving explicitly the conformal Hamada operator in any d. Some singularities in construction for dimensions $$d=2$$ d = 2 and $$d=4$$ d = 4 are noticed. We also prove a general theorem that a scalar conformal operator with n derivatives in $$d=n-2$$ d = n - 2 dimensions is impossible to construct. Finally, we compare our explicit construction with the one that uses conformal covariant derivatives and conformal curvature tensors. We present new results for operators built with different orders of conformal covariant derivatives.

Observable strong field effects of extra spacetime dimension in the braneworld black hole

Inspired by the string theory, the braneworld picture introduces extra dimensions beyond the four that may have observable non-trivial effects in short distance (strong field) gravity experiments. A case in point is the Randall–Sundrum braneworld picture that projects the 5d bulk Weyl tensor onto the 3d brane providing a stress tensor in the effective Einstein field equations on the brane. Dadhich, Maartens, Papadopoulos and Rezania (DMPR) derived an exact braneworld black hole solution of the brane vacuum field equations. The solution formally resembles that of Reissner–Nordström but is physically different from it since the ”tidal charge” Υ in the solution is not the electric charge but an imprint from the fifth dimension allowing both signs in the power law modification ±Υ2r2 to the Schwarzschild metric Υ=0. The corresponding black holes are designated as DMPR±. We study here the effect of Υ on strong field lensing observables and compare in the eikonal limit the ring down quasinormal mode (QNM) frequencies of DMPR− with those of DMPR＋ , the two variants of tidal charge modified Schwarzschild black hole (Υ=0). It turns out that the tidal charge can significantly modify the Schwarzschild lensing observables and QNM frequencies. In particular, we find that the Pretorius–Khurana critical exponent γ of circular null orbits in the DMPR− black hole has a lower value than that for the Schwarzschild black hole, which indicates a stronger Lyapunov instability suggesting that the accretion disks of DMPR− black holes would appear brighter. The case of the SgrA* black hole is considered for a possible constraint on Υ from the EHT observation of its shadow size.

Black hole evaporation process and Tangherlini–Reissner–Nordström black holes shadow

In this article, we study the black hole evaporation process and shadow property of the Tangherlini-Reissner-Nordström (TRN) black holes. The TRN black holes are the higher-dimensional extension of the Reissner-Nordström (RN) black holes and are characterized by their mass M, charge q, and spacetime dimensions D. In higher-dimensional spacetime, the black hole evaporation occurs rapidly, causing the black hole’s horizon to shrink. We derive the rate of mass loss for the higher-dimensional charged black hole and investigate the effect of higher-dimensional spacetime on charged black hole shadow. We derive the complete geodesic equations of motion with the effect of spacetime dimensions D. We determine impact parameters by maximizing the black hole’s effective potential and estimate the critical radius of photon orbits. The photon orbits around the black hole shrink with the effect of the increasing number of spacetime dimensions. To visualize the shadows of the black hole, we derive the celestial coordinates in terms of the black hole parameters. We use the observed results of M87 and Sgr A∗ black hole from the Event Horizon Telescope and estimate the angular diameter of the charge black hole shadow in the higher-dimensional spacetime. We also estimate the energy emission rate of the black hole. Our finding shows that the angular diameter of the black hole shadow decreases with the increasing number of spacetime dimensions D.

Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field Theory

The asymptotic strong-coupling behavior as well as the exact critical exponents from scalar field theory even for the simplest case of 1+1 dimensions have not been obtained yet. Hagen Kleinert has linked both critical exponents and strong coupling parameters to each other. He used a variational technique ( back to kleinert and Feynman) to extract accurate values for the strong coupling parameters from which he was able to extract precise critical exponents. In this work, we suggest a simple method of using the effective potential ( low order) to obtain exact values for the strong-coupling parameters for the ϕ4 scalar field theory in 0+1 and 1+1 space–time dimensions. For the 0+1 case, our results coincide with the well-known exact values already known from literature while for the 1+1 case we test the results by obtaining the corresponding exact critical exponent. As the effective potential is a well-established tool in quantum field theory, we expect that the results can be easily extended to the most important three dimensional case and then the dream of getting exact critical exponents is made possible.

New asymptotically (anti)-de Sitter black holes in (super)gravity

We use the duality between gravitational dynamics and fluids living on dynamical surfaces carrying multiple charges, known as the blackfold approach, to perturbatively construct new asymptotically global (Anti)-de Sitter multi-spinning, non-extremal, multi-charged black holes in theories of higher-dimensional gravity minimally coupled to a dilaton and higher-form gauge fields in spacetime dimensions D ≥ 5, and new asymptotically AdSl × Sm black holes in type IIB and eleven-dimensional supergravity. These solutions include the generalisation of the Kerr-Newman solution to (A)dS carrying either electric or string charge, generalisations of black rings to higher-dimensions with \U0001d54ap × \U0001d54an+1 horizon topology, static de Sitter solutions carrying arbitrary q-brane charge, as well as various asymptotically AdSl× Sm multi-charged and multi-spinning black hole solutions, some of which correspond to novel thermal states in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 Super-Yang-Mills theory.

Chronotopes of Transnational Literacies: How Youth Live and Imagine Social Worlds in their Digital Media Practices

AbstractThis study explores the transnational literacies that contribute to creating online social connections among migrant youth that may support their development and navigation of life across countries. We examine how social connectedness is semiotically constructed through time–space framing among two youth of Chinese descent who were participants of a larger study of the digital media practices of young people in an urban high school. We build on the concept of chronotope (Bakhtin, 1981) and scholarship of transnational literacies to understand the space–time dimensions of digital literacy practices, specifically how youth create the spatiotemporal context or frame of reference for their actions and positionings with others across geographical distances. Using a case study approach with data from interviews and observations, we analyzed how the youth depicted their transnational social relations within particular time–space frames. Qualitative and discourse analyses of the youths' narrative accounts show that they positioned themselves in proximity with their transnational peers within particular time–space contexts that supported their actions and emotions, and how they made sense of events, issues, practices, and their own identities as transnational individuals. The youths' ideas of schooling and education, and attunement to nationalistic ideologies, were developed through multiple chronotopes in their social connections across countries. This study offers implications for how an attention to the transnational spatiotemporal frame of youths' discourse and narrative may give us a more nuanced understanding of the subjectivity, knowledge, and perspective they derive from their experiences of movement and connection across borders.

Defect fusion and Casimir energy in higher dimensions

We study the operator algebra of extended conformal defects in more than two spacetime dimensions. Such algebra structure encodes the combined effect of multiple impurities on physical observables at long distances as well as the interactions among the impurities. These features are formalized by a fusion product which we define for a pair of defects, after isolating divergences that capture the effective potential between the defects, which generalizes the usual Casimir energy. We discuss general properties of the corresponding fusion algebra and contrast with the more familiar cases that involve topological defects. We also describe the relation to a different defect setup in the shape of a wedge. We provide explicit examples to illustrate these properties using line defects and interfaces in the Wilson-Fisher CFT and the Gross-Neveu(-Yukawa) CFT and determine the defect fusion data thereof.