Scalar Field Research Articles

Scale symmetry breaking and generation of mass at quantum critical points

We study an asymptotically free theory of N relativistic Dirac fermions and a real scalar field coupled by Yukawa and scalar self-interactions in three dimensions using functional renormalisation. In the limit of many fermion flavours, the cubic scalar coupling becomes exactly marginal due to quantum fluctuations, leading to a line of strongly-coupled infrared fixed points. Fermion mass can be generated through a quantum phase transition even if chiral symmetry is absent. The line of fixed points terminates at a critical endpoint due to the loss of vacuum stability. Exactly at the endpoint, scale symmetry is broken spontaneously, leading to the generation of fermion mass. Intriguingly, the absence of chiral symmetry is a prerequisite for the spontaneous generation of fermion mass, and not a consequence thereof. We also highlight close similarities between Gross-Neveu and Gross-Neveu-Yukawa theories at and away from critical points, and establish the large-N equivalence of their functional RG flows and quantum effective actions. Further implications including for conformal field theories are indicated.

Scalarization of Kerr–Newman black holes in the Einstein–Chern–Simons-scalar theory

We investigate the tachyonic instability of Kerr–Newman (KN) black hole with a rotation parameter a in the Einstein–Chern–Simons-scalar theory coupled with a quadratic massive scalar field. This instability analysis corresponds to exploring the onset of spontaneous scalarization for KN black holes. First, we find no a-bound for α<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha <0$$\\end{document} case by considering (1 + 1)-dimensional analytical method. A direct numerical method is adopted to explore (2 + 1)-dimensional time evolution of a massive scalar perturbation with positive and negative α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} to obtain threshold curves numerically. We obtain threshold curves αth(a)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _{\ extrm{th}}(a)$$\\end{document} of tachyonic instability for positive α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} without any a-bounds. We expect to find the same threshold curves αth(a)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _{\ extrm{th}}(a)$$\\end{document} of tachyonic instability for negative α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} without any a-bound because its linearized scalar theory is invariant under the transformation of α→-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\rightarrow -\\alpha $$\\end{document} and θ→-θ.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta \\rightarrow -\ heta .$$\\end{document} In addition, it is found that the scalar mass term suppresses tachyonic instability of KN black holes, while the black hole charge promotes the instability (disregarding the contribution of the charge to the existence conditions M2-Q2≥a2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M^2-Q^2\\ge a^2)$$\\end{document}.

Classical Kerr-Schild double copy in bigravity for maximally symmetric spacetimes

A generalized Kerr-Schild ansatz for bigravity, already considered in the literature, which leads to linear interactions between the metrics is used to study the bigravity equations in the context of the double copy. By contracting the resulting spin-2 field bigravity equations of motion using Killing vector fields, as is usually carried out in general relativity, we arrive to the single and zeroth copy equations for the mentioned ansatz. For the case of stationary solutions, we obtain two Maxwell and two conformally coupled scalar field equations for the single and zeroth copies respectively, and the linear interactions are absent. In the time-dependent case we obtain equations for the fields which are coupled. By decoupling these equations and at the zeroth copy level, we recover a massless and a massive field whose mass is proportional to the Fierz-Pauli mass and depends on the coefficients of the interaction potential between the metrics. This has been also previously documented in the literature and is now reinterpreted within the context of the double copy proposal.

Charmonium production in hot magnetized hyperonic matter: Effects of the baryonic Dirac sea and pseudoscalar-vector mixing

We investigate the medium modifications of the masses of pseudoscalar open charm (D and D¯) mesons and the charmonium state [ψ(3770)] in hot isospin asymmetric strange hadronic medium in the presence of an external magnetic field within a chiral effective model. The in-medium partial decay widths of ψ(3770) to charged and neutral DD¯ mesons are computed from the medium modifications of the masses of the initial and final state mesons. These are computed using two light quark pair creation models—(I) the P03 model and (II) a field theoretical (FT) model of composite hadrons with quark (and antiquark) constituents. The production cross sections of ψ(3770), arising from scattering of the D and D¯ mesons, are computed from the relativistic Breit-Wigner spectral function expressed in terms of the in-medium masses and the decay widths of the charmonium state. The effects of the magnetic field are considered due to the Dirac sea (DS) of the baryons, the mixing of the pseudoscalar (S=0) and vector (S=1) meson (PV mixing), the Landau level contributions for the charged hadrons. The anomalous magnetic moments (AMMs) of the baryons are also taken into account in the present study. For magnetized nuclear matter, at ρB=ρ0, the effect of Dirac sea leads to inverse magnetic catalysis (IMC), which is drop of the magnitude of the light quark condensates (proportional to the scalar fields) with increase in the magnetic field, contrary to the opposite effect of magnetic catalysis (MC) at ρB=0. The inclusion of hyperons to the nuclear medium is observed to lead to magnetic catalysis. There are observed to be significant effects from the DS and PV mixing on the properties of the charm mesons. The production cross sections of ψ(3770) arising due to scattering of D+D−(D0D¯0) mesons in the hot magnetized strange hadronic matter are observed to have distinct peak positions, when the magnetic field is large. This is because the production cross sections have contributions from the transverse as well as longitudinal components of ψ(3770), which have nondegenerate masses due to PV [ψ(3770)−ηc′] mixing. These can have observable consequences on the dilepton spectra as well as on the production of the charm mesons in ultrarelativistic peripheral heavy ion collision experiments, where the produced magnetic field is huge. Published by the American Physical Society 2024

Constant-roll inflation with tachyon field in the holographic braneworld

Abstract We study inflation driven by the tachyon field in the holographic braneworld by assuming the second slow-roll parameter η is constant. The parameter η can be either defined by the tachyon scalar field and the Hubble parameter or by the Hubble parameter only. By assuming a constant η, we derive and numerically solve a differential equation for the Hubble expansion rate. We calculate numerically the scalar spectral index and the tensor-to-scalar ratio. We confront the results with the observational data and find some constraints on the free model parameters. The swampland conjectures are discussed in the context of the constant-roll inflation, with some accent on the holographic model.

Weakly guiding approximation of a three-dimensional waveguide model for extreme ultraviolet lithography simulation

A three-dimensional (3D) waveguide model is applied in extreme ultraviolet (EUV) lithography simulations. The 3D waveguide model is equivalent to rigorous coupled-wave analysis, but fewer field components are used to solve Maxwell’s equations. The 3D waveguide model uses two components of vector potential, A x and A y , corresponding to the two polarizations. The electric field of the A x polarization is approximately parallel to the x axis, and the electric field of the A y polarization is approximately parallel to the y axis. The 3D waveguide model solves a coupled vector wave equation for two polarizations. The refractive index of conventional EUV absorbers is close to that of vacuum. The weakly guiding approximation in optical fiber theory is applied to the 3D waveguide model. The coupled vector wave equations for the two polarizations are decoupled into two independent scalar wave equations. Maxwell’s equations are simplified to a set of scalar wave equations. The weakly guiding approximation reduces the computation time to solve the equations. The computation time required to solve the weakly guiding approximation is about 1/5 of the time to solve the original 3D waveguide model.

Hypergeometric Gevrey-0 approximation for the Gevrey-k divergent series with application to eight-loop renormalization group functions of the O(N)-symmetric field model

Mera et al. (Phys Rev Lett 115:143001, 2015) discovered that the hypergeometric function 2F1(a1,a2;b1;ωg)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}_2F_1(a_1,a_2;b_1; \\omega g)$$\\end{document} can serve as an accurate approximant for a divergent Gevrey-1 type of series with an asymptotic large-order behavior of the form n!nbσn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n! n^b \\sigma ^n$$\\end{document}. What is strange about this approximant is that it has a series expansion with the wrong large-order behavior (Gevrey-0 type). In this work, we extend this discovery to Gevrey-k series where we show that the hypergeometric approximants and its extension to the generalized hypergeometric approximants are not only able to approximate divergent (Gevrey-1) series but also able to approximate strongly-divergent series of Gevrey-k type with k=2,3,…\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=2,3,\\ldots$$\\end{document}. Moreover, we show that these hypergeometric approximants are able to predict accurate results for the non-perturbative strong-coupling and large-order parameters from weak-coupling data as input. Examples studied here are the ground-state energy for the xn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x^n$$\\end{document} anharmonic oscillators. The hypergeometric approximants are also used to approximate the recent eight-loop series ( g-expansion) of the renormalization group functions for the O(N)-symmetric ϕ4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi ^4$$\\end{document} scalar field model. Form these functions for N=0,1,2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=0, 1, 2$$\\end{document}, and 3, critical exponents are extracted which are very competitive to results from more sophisticated approximation techniques.

Achieving Optimal Order in a Novel Family of Numerical Methods: Insights from Convergence and Dynamical Analysis Results

In this manuscript, we introduce a novel parametric family of multistep iterative methods designed to solve nonlinear equations. This family is derived from a damped Newton’s scheme but includes an additional Newton step with a weight function and a “frozen” derivative, that is, the same derivative than in the previous step. Initially, we develop a quad-parametric class with a first-order convergence rate. Subsequently, by restricting one of its parameters, we accelerate the convergence to achieve a third-order uni-parametric family. We thoroughly investigate the convergence properties of this final class of iterative methods, assess its stability through dynamical tools, and evaluate its performance on a set of test problems. We conclude that there exists one optimal fourth-order member of this class, in the sense of Kung–Traub’s conjecture. Our analysis includes stability surfaces and dynamical planes, revealing the intricate nature of this family. Notably, our exploration of stability surfaces enables the identification of specific family members suitable for scalar functions with a challenging convergence behavior, as they may exhibit periodical orbits and fixed points with attracting behavior in their corresponding dynamical planes. Furthermore, our dynamical study finds members of the family of iterative methods with exceptional stability. This property allows us to converge to the solution of practical problem-solving applications even from initial estimations very far from the solution. We confirm our findings with various numerical tests, demonstrating the efficiency and reliability of the presented family of iterative methods.

Quasinormal modes, Hawking radiation and absorption of the massless scalar field for Reissner–Nordström black hole surrounded by a cloud of strings in Rastall gravity

In this work, we investigate the quasinormal modes (QNMs), shadow radius, gray-body factor, Hawking radiation and absorption cross-section of the Reissner–Nordström black hole surrounded by a cloud of strings in Rastall gravity for a massless scalar field. We use the sixth-order Wenzel, Kramers and Brillouin (WKB) and unstable circular null geodesic methods to calculate QNMs. Moreover, the values obtained by the two methods are in very good agreement. The real part and absolute value of imaginary part of quasinormal frequencies decrease with the increase of [Formula: see text]. As [Formula: see text] increases, the real part of quasinormal frequencies increases while the absolute value of imaginary part first increases and then decreases. For [Formula: see text], they decrease with the increase of [Formula: see text]. While they first increase and then decrease with [Formula: see text] increasing at small value of [Formula: see text] when [Formula: see text]. Then using the unstable circular null geodesic method, we obtain the shadow radius of black hole. We find that shadow radius decreases first and then increases as the negative parameter [Formula: see text] increases. We also calculate the gray-body factor. According to it, Hawking radiation and absorption cross-section are calculated. We explore the influence of [Formula: see text], [Formula: see text] and [Formula: see text] on the energy emission rate. When other parameters are fixed, the black hole lives longer as [Formula: see text], positive parameter [Formula: see text] and [Formula: see text] increase. To obtain absorption cross-section, we adopt the partial wave method and sinc approximation method, and the results obtained by two methods have excellent consistency at mid-high frequency region. Further, we assess the effect of [Formula: see text], [Formula: see text] and [Formula: see text] on the absorption cross-section.

Scalar fields, localized structures and the Starobinsky model

This work deals with the presence of localized static structures in the real line, described by relativistic real scalar fields in two spacetime dimensions. We consider models featuring both standard and modified kinematics, where we employ two intriguing potentials supporting defect solutions. The first potential can transform kink into compacton in the standard framework, while the second one is based on the inflationary Starobinsky model. Interesting possibilities unseen in previous investigations are described, in particular, for the case related to the Starobinsky potential. The addressed potentials are inserted into a broader framework, and so the extended models are described by a wider set of solutions. This investigation also reveals the presence of the twinlike behaviour for a specific compact configuration, which solves two distinct models.

Can the induced increase in the angular velocity prevent the overspinning of BTZ black holes?

Previously we showed that nearly extremal Bañados–Teitelboim–Zanelli (BTZ) black holes can be overspun by test bodies and fields, following the work of Rocha and Cardoso for the extremal case. The naked singularities in AdS space-times correspond to states rotating faster than light in the Ads/CFT correspondence. Therefore, overspinning turns out to be a drastic problem in a (2 + 1) dimensional AdS space-time, where one cannot invoke backreaction effects. Here, we consider the induced increase in the angular velocity of the event horizon which modifies the condition to allow the absorption of the perturbations satisfying the null energy condition. We show that its magnitude is sufficiently large to prevent the absorption of the challenging modes both for test bodies and scalar fields. We bring a solution to the notorious overspinning problem which does not involve any reference to self-energy or gravitational radiation

Low spin solutions of higher spin gravity: BPST instanton

Higher spin gravities do not have a low energy limit where higher-spin fields decouple from gravity. Nevertheless, it is possible to construct fine-tuned exact solutions that activate low-spin fields without sourcing the higher-spin fields. We show that BPST (Belavin-Polyakov-Schwartz-Tyupkin) instanton is an exact solution of Chiral Higher Spin Gravity, i.e. it is also a solution of the holographic dual of Chern-Simons matter theories. This gives an example of a low-spin solution. The instanton sources the opposite helicity spin-one field and a scalar field. We derive an Effective Field Theory that describes the coupling between an instanton and the other two fields, whose action starts with the Chalmers-Siegel action and has certain higher derivative couplings.

A regular MOG black hole’s impact on shadows and gravitational weak lensing in the presence of a quintessence field

We investigate the impact of the modified gravity (MOG) field and the quintessence scalar field on horizon evolution, black hole (BH) shadow and the weak gravitational lensing around a static spherically symmetric BH. We first begin to write the BH metric associated with the MOG parameter and quintessence scalar field. We then determine the BH shadow and obtain numerical solutions for the photon sphere and shadow radius. We show that the MOG (α) and the quintessence (c) parameters have a significant impact on the BH shadow and photon sphere. Based on the analysis, we further show that the combined effects of the MOG parameter and quintessence field can increase the values of BH shadow and photon sphere radii. We also obtain constraints on the BH parameters by applying the observational data of Sgr A⋆ and M87⋆. Finally, we consider the weak deflection angle of BH within the context of the Gauss–Bonnet theorem (GBT) and show that the combined effects of the MOG and quintessence parameters do make the value of the deflection angle increase, and find this remarkable property is in good agreement with the physical meaning of both parameters that can maintain the strong gravitational field in the surrounding environment of a BH.

Five-dimensional Myers-Perry black holes under massive scalar perturbation: bound states and quasinormal modes

Abstract The stability of five-dimensional singly rotating Myers-Perry Black Holes against massive scalar perturbations is studied. &amp;#xD;Both the quasibound states and quasinormal modes of the massive scalar field are considered. For the quasibound states, we use an analytical method to discuss the effective potential felt by the scalar field, and found that there is no potential well outside the event horizon. Thus, &amp;#xD;singly rotating Myers-Perry Black Holes are stable against the perturbation of quasibound states of massive scalar fields. &amp;#xD;Then, we use continued fraction method based on solving a seven-term recurrence relations to compute the spectra of the quasinormal modes.&amp;#xD;For different values of the black hole rotation parameter $a$, scalar mass parameter $\mu$ and angular quantum numbers, all found quasinormal modes&amp;#xD;are damped. Besides, when the scalar mass $\mu$ becomes relatively large, the long-living quasiresonances are also found as in other rotating black hole models. &amp;#xD;Our results complement previous arguments on the stability of five-dimensional singly rotating Myers-Perry black holes against massive scalar perturbations.

Soft theorems for boostless amplitudes

We consider effective field theories (EFTs) of scalar fields with broken Lorentz boosts, which arise by taking the decoupling and flat-space limits of the EFT of inflation, and derive constraints that must be satisfied by the corresponding scattering amplitudes if there is an underlying non-linearly realised symmetry. We primarily concentrate on extended shift symmetries which depend on the space-time coordinates, and find that combinations of scattering amplitudes obey enhanced Adler zeros. That is, such combinations vanish as one external momentum is taken soft, with the rate at which they vanish dictated by the corresponding symmetry. In our soft theorem derivation, we pay particular care to the energy and momentum-conserving delta functions that arise due to space-time translations, and show that when acted upon by derivatives with respect to spatial momenta, they yield a tower of soft theorems which are ultimately required for closure of the underlying symmetry algebra. All of our soft theorems correspond to constraints that must be satisfied by on-shell amplitudes and, even for symmetries that depend on the time coordinate, our soft theorems only require derivatives to be taken with respect to spatial momenta. We perform a soft bootstrap procedure to find solutions to our soft theorems, and compare these solutions to what we find from an off-shell analysis using the coset construction.

Hybrid model of condensate and particle dark matter: Linear perturbations in the hydrodynamic limit

We analyze perturbations of self-interacting, scalar field dark matter that contains modes in both a coherent condensate state and an incoherent particlelike state. Starting from the coupled equations for the condensate, the particles’ phase-space distribution, and their mutual gravitational potential, first derived from first principles in earlier work by the authors, we derive a hydrodynamic limit of two coupled fluids and study their linearized density perturbations in an expanding universe, also including particle pressure under an assumption for an equation of state consistent with the dynamical equations. We find that away from the condensate-only or particle-only limits, and for certain ranges of the parameters, such self-interacting mixtures can significantly enhance the density power spectrum above the standard linear ΛCDM value at localized wave numbers, even pushing structure formation into the nonlinear regime earlier than expected in ΛCDM for these scales. We also note that such mixtures can lead to degeneracies between models with different boson masses and self-coupling strengths, in particular, between self-coupled models and noncoupled fuzzy dark matter made up of heavier bosons. These findings open up the possibility of a richer phenomenology in scalar field dark matter models and could further inform efforts to place observational limits on their parameters. Published by the American Physical Society 2024

Possibility of the Traversable Wormholes in the Galactic Halos within 4D Einstein–Gauss–Bonnet Gravity

AbstractRecently, there has been significant interest regarding the regularization of a limit of Einstein–Gauss–Bonnet (EGB) gravity. This regularization involves re‐scaling the Gauss–Bonnet (GB) coupling constant as , which bypasses Lovelock's theorem and avoids Ostrogradsky instability. A noteworthy observation is that the maximally or spherically symmetric solutions for all the regularized gravities coincide in the scenario. Considering this, the wormhole solutions in the galactic halos are investigated based on three different choices of dark matter (DM) profiles, such as Universal Rotation Curve, Navarro–Frenk–White, and Scalar Field Dark Matter with the framework of EGB gravity. Also, the Karmarkar condition is used to find the exact solutions for the shape functions under different non‐constant redshift functions. The energy conditions for each DM profile are discussed and the influence of GB coefficient in violating energy conditions are noticed, especially null energy conditions. Further, some physical features of wormholes, viz. complexity factor, active gravitational mass, total gravitational energy, and embedding diagrams, have been explored.

Field theory equivalences as spans of L∞ -algebras

Semi-classically equivalent field theories are related by a quasi-isomorphism between their underlying L∞ -algebras, but such a quasi-isomorphism is not necessarily a homotopy transfer. We demonstrate that all quasi-isomorphisms can be lifted to spans of L∞ -algebras in which the quasi-isomorphic L∞ -algebras are obtained from a correspondence L∞ -algebra by a homotopy transfer. Our construction is very useful: homotopy transfer is computationally tractable, and physically, it amounts to integrating out fields in a Feynman diagram expansion. Spans of L∞ -algebras allow for a clean definition of quasi-isomorphisms of cyclic L∞ -algebras. Furthermore, they appear naturally in many contexts within physics. As examples, we first consider scalar field theory with interaction vertices blown up in different ways. We then show that (non-Abelian) T-duality can be seen as a span of L∞ -algebras, and we provide full details in the case of the principal chiral model. We also present the relevant span of L∞ -algebras for the Penrose–Ward transform in the context of self-dual Yang–Mills theory and Bogomolny monopoles.

Thermal fluctuations, deflection angle and greybody factor of a high-dimensional Schwarzschild black hole in STVG

Abstract In this work, we study the thermal fluctuations, deflection angle and greybody factor of the high-dimensional Schwarzschild black hole in scalar-tensor-vector gravity (STVG). We calculate some thermodynamic quantities related to the correction of black hole entropy caused by thermal fluctuations and discuss the effect of the correction parameters on these quantities. By analysing the changes in the corrected specific heat, we find that thermal fluctuations make the small-sized black hole more stable. It is worth noting that the STVG parameter does not affect the thermodynamic stability of this black hole. Additionally, by utilizing the Gauss-Bonnet theorem, the deflection angle is obtained in the weak field limit and the effect of two parameters on the results is visualized. Finally, we calculate the bounds on greybody factor of a massless scalar field. We observe that as the STVG parameter around black hole increases, the weak deflection angle becomes larger and the more scalar particles can reach infinity. However, the spacetime dimension has the opposite effect to the STVG parameter on the weak deflection angle and greybody factor.

Techniques for Solving Static Klein-Gordon Equation with Self-Interaction λϕ4 and Arbitrary Spherical Source Terms

The Klein-Gordon equation for a scalar field sourced by a static spherically symmetric background is an interesting second-order differential equation with applications in particle physics, astrophysics, and elsewhere. Here we present static solutions for generic source density profiles in the case where the scalar field has no interactions or a mass term. For a λϕ4 self-interaction term, we develop the techniques that are necessary numerical computation. We also provide code to perform the numerical calculations that can be adapted for arbitrary density profiles. ▪