Massless Modes Research Articles

Strong cosmic censorship in de Sitter spacetimes with dark matter

After imposing the weak energy condition on dark matter, we find that even in the absence of charge, a spherically symmetric de Sitter black hole with perfect fluid dark matter may still possess a Cauchy horizon. This paper investigates the stability of the Cauchy horizon in such a black hole under perturbations from a massless scalar field. Through numerical calculations of the massless scalar field's quasinormal modes, we discover that in this spacetime, when the black hole approaches extremality, i.e., when the dark-matter parameter b approaches its maximum value bmax, the Strong Cosmic Censorship (SCC) conjecture may be violated. This is the first instance of classical SCC violation observed in a spherically symmetric, uncharged black hole. Additionally, we explore the region of SCC violation within the parameter space ΛM2−b/bmax. Our findings indicate that as the cosmological constant increases, the violation region initially expands and then contracts.

Matter coupled to 3d quantum gravity: one-loop unitarity

Abstract We expect quantum field theories for matter to acquire intricate corrections due to their coupling to quantum fluctuations of the gravitational field. This can be precisely worked out in 3d quantum gravity: after integrating out quantum gravity, matter fields are effectively described as noncommutative quantum field theories, with quantum-deformed Lorentz symmetries. An open question remains: Are such theories unitary or not? On the one hand, since these are effective field theories obtained after integrating out high energy degrees of freedom, we may expect the loss of unitarity. On the other hand, as rigorously defined field theories built with Lorentz symmetries and standing on their own, we naturally expect the conservation of unitarity. In an effort to settle this issue, we explicitly check unitarity for a scalar field at one-loop level in both Euclidean and Lorentzian space-time signatures. We find that unitarity requires adding an extra-term to the propagator of the noncommutative theory, corresponding to a massless mode and given by a representation with vanishing Plancherel measure, thus usually ignored in spinfoam path integrals for quantum gravity. This indicates that the inclusion of matter in spinfoam models, and more generally in quantum gravity, might be more subtle than previously thought.

New mechanism for fermion localization in the presence of anti-curvature tensor

This study aims into brane-world scenarios within the framework of f(R, A) gravity called Ricci-inverse modified theory, exploring the dynamics of spin-1/2 fermions coupled non-minimally to background scalar field functions. Through theoretical analysis and numerical techniques, we investigate the localization of both massless and massive fermionic modes on the brane. Our findings shows intricate phenomena, including unexpected configurations of the effective potentials and the identification of resonance modes in massive fermionic spectra. These insights shed light on the interplay between modified gravity and matter in extra-dimensional models, offering promising avenues for experimental validation and furthering our understanding of fundamental physics.

Nambu-Goldstone modes in magnetized T2n extra dimensions

We consider a U(1) gauge theory on M4×T4 with background magnetic fluxes. We show that a theory including arbitrary fluxes can always be studied in a theory involving only diagonal fluxes by appropriate coordinate transformations. It is found that the number of independent magnetic fluxes is equal to the rank of the classical value of the field strength matrix, rank⟨F⟩. The number of massless zero modes induced from extra components of higher-dimensional gauge field (Wilson-line scalar field) is also determined by rank⟨F⟩. We explicitly confirm that the quantum corrections due to the matter fermion to the squared mass of the Wilson-line scalar field cancel out at the one-loop level. For this purpose, we derive the fermion mass spectrum on M4×T4 with arbitrary fluxes. By taking the flux diagonal basis, creation and annihilation operators for Kaluza-Klein quantum numbers are defined appropriately. Our results are easily generalized to the case of M4×T2n(n≥3). Published by the American Physical Society 2024

Medium induced mixing, spatial modulations, and critical modes in QCD

The mixing between the chiral condensate and the density in hot and dense quantum chromodynamics (QCD) matter is familiar. We show that the mixing relevant for the ground state is considerably more extensive, and in particular also involves gluonic degrees of freedom. As a result, the Hessian of the QCD effective action is non-Hermitian, but retains a symmetry under combined charge and complex conjugation. This can lead to complex-conjugate pairs of eigenvalues of this Hessian, signaling regimes with spatially modulated correlations. Furthermore, based on the analytic structure of the quark determinant at a chiral critical point, we demonstrate that the corresponding massless critical mode is composed of the chiral condensate, the density and the Polyakov loops. Due to an avoided crossing, the critical mode turns out to be disconnected from the chiral condensate in vacuum. We present general arguments for all these features and illustrate them through explicit model calculations. Published by the American Physical Society 2024

Anomalous dimension and quasinormal modes of flavor branes

We study scalar quasinormal modes in a D3/D7 system holographically dual to a quantum field theory with chiral symmetry breaking at finite temperature. From the bottom-up approach, we consider a nontrivial dilaton profile which is responsible for the anomalous dimension of the quark condensate. It depends on a new parameter q in the model. By varying this parameter, we study the behavior of the massive and massless scalar quasinormal modes. The numerical method that we use is the spectral method, and we find that there is no pure imaginary mode for the massless case but it appears by increasing the parameter q. It is known that this mode becomes tachyonic for massive cases. Then we turn on a pseudoscalar field and using a simple ansatz study its effect on the quasinormal modes of the scalar field. By varying the parameter of the nontrivial dilaton profile in the model, we qualitatively study quasinormal modes in walking theories.

Holographic fluids from 5D dilaton gravity

We study a solvable class of five-dimensional dilaton gravity models that continuously interpolate between anti-de Sitter (AdS5), linear dilaton (LD5) and positively curved spacetimes as a function of a continuous parameter ν. The dilaton vacuum expectation value is set by a potential localized on a flat brane. We chart the elementary properties of these backgrounds for any admissible ν, and determine stability conditions of the brane-dilaton system. We find that the spectrum of metric fluctuations can be either continuous or discrete. It features a massless graviton mode confined between the brane and the curvature singularity, and a massive radion mode tied to brane-dilaton stability. We show that, in the presence of a bulk black hole, the holographic theory living on the brane features a perfect fluid. The equation of state of the holographic fluid interpolates between radiation, pressureless matter and vacuum energy as a function of ν. This extends earlier findings on holographic fluids. Our results suggest that the thermodynamics of the fluid mirrors precisely the thermodynamics of the bulk black hole.

Spin-(s, j) projectors and gauge-invariant spin-s actions in maximally symmetric backgrounds

Given a maximally symmetric d-dimensional background with isometry algebra g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathfrak{g} $$\\end{document}, a symmetric and traceless rank-s field ϕa(s) satisfying the massive Klein-Gordon equation furnishes a collection of massive g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathfrak{g} $$\\end{document}-representations with spins j ∈ {0, 1, · · · , s}. In this paper we construct the spin-(s, j) projectors, which are operators that isolate the part of ϕa(s) that furnishes the representation from this collection carrying spin j. In the case of an (anti-)de Sitter ((A)dSd) background, we find that the poles of the projectors encode information about (partially-)massless representations, in agreement with observations made earlier in d = 3, 4. We then use these projectors to facilitate a systematic derivation of two-derivative actions with a propagating massless spin-s mode. In addition to reproducing the massless spin-s Fronsdal action, this analysis generates new actions possessing higher-depth gauge symmetry. In (A)dSd we also derive the action for a partially-massless spin-s depth-t field with 1 ≤ t ≤ s. The latter utilises the minimum number of auxiliary fields, and corresponds to the action originally proposed by Zinoviev after gauging away all Stückelberg fields. Some higher-derivative actions are also presented, and in d = 3 are used to construct (i) generalised higher-spin Cotton tensors in (A)dS3; and (ii) topologically-massive actions with higher-depth gauge symmetry. Finally, in four-dimensional 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} = 1 Minkowski superspace, we provide closed-form expressions for the analogous superprojectors.

Aharonov-Bohm effect in Generalized Electrodynamics

The Aharonov-Bohm (AB) effect is considered in the context of Generalized Electrodynamics (GE) by Podolsky and Bopp. GE is the only extension to Maxwell electrodynamics that is locally U(1)-gauge invariant, admits linear field equations and contains higher-order derivatives of the vector potential. GE admits both massless and massive modes for the photon. We recover the ordinary quantum phase shift of the AB effect, derived in the context of Maxwell electrodynamics, for the massless mode of the photon in GE. The massive mode induces a correction factor to the AB phase shift depending on the photon mass. We study both the magnetic AB effect and its electric counterpart. In principle, accurate experimental observations of AB the phase shift could be used to constrain GE photon mass.

Braneworlds in warped Einsteinian cubic gravity

Einstenian cubic gravity (ECG) is a modified theory of gravity constructed with cubic contractions of the curvature tensor. This theory has the remarkable feature of having the same two propagating degrees of freedom of Einstein gravity (EG), at the perturbative level on maximally symmetric spacetimes. The additional unstable modes steaming from the higher order derivative dynamics are suppressed provided that we consider the ECG as an effective field theory wherein the cubic terms are seen as perturbative corrections of the Einstein-Hilbert term. Extensions of ECG have been proposed in cosmology and compact objects in order to probe if this property holds in more general configurations. In this work, we construct a modified ECG gravity in a five dimensional warped braneworld scenario. By assuming a specific combination of the cubic parameters, we obtained modified gravity equations of motion with terms up to second-order. For a thin 3-brane, the cubic-gravity corrections yield an effective positive bulk cosmological constant. Thus, in order to keep the 5D bulk warped compact, an upper bound of the cubic parameter with respect to the bulk curvature was imposed. For a thick brane, the cubic-gravity terms modify the scalar field potential and its corresponding vacuum. Nonetheless, the domain-wall structure with a localized source is preserved. At the perturbative level, the Kaluza-Klein (KK) tensor gravitational modes are stable and possess a localized massless mode provided the cubic corrections are small compared to the EG braneworld.

A Lattice Formulation of Weyl Fermions on a Single Curved Surface

Abstract In the standard lattice domain-wall fermion formulation, one needs two flat domain-walls where both of the left- and right-handed massless modes appear. In this work we investigate a single domain-wall system with a nontrivial curved background. Specifically we consider a massive fermion on a 3D square lattice, whose domain-wall is a 2D sphere. In the free theory, we find that a single Weyl fermion is localized at the wall and it feels gravity through the induced spin connection. With a topologically nontrivial U(1) link gauge field, however, we find a zero mode with the opposite chirality localized at the center where the gauge field is singular. In the latter case, the low-energy effective theory is not chiral but vectorlike. We discuss how to circumvent this obstacle in formulating lattice chiral gauge theory in the single domain-wall fermion system.

Thick Branes in Horndeski Gravity

We investigate thick brane solutions in the Horndeski gravity. In this setup, we found analytical solutions, applying the first-order formalism to two scalar fields where the first field comes from the nonminimal scalar-tensor coupling and the second is due to the matter contribution sector. With these analytical solutions, we evaluate the symmetric thick brane solutions in Horndeski gravity with four-dimensional geometry. In such a setup, we evaluate the gravity fluctuations to find “almost massless modes,” for any values of the Horndeski parameters. These modes were used to compute the corrections to the Newtonian potential and evaluate the limit four-dimensional gravity.

Higgs-like (pseudo)scalars in AdS4, marginal and irrelevant deformations in CFT3, and instantons on S 3

Employing a 4-form ansatz of 11-dimensional supergravity over a non-dynamical background and setting the internal space as an Hopf fibration on , we obtain a consistent truncation. The (pseudo)scalars, in the resulting scalar equations in Euclidean AdS space, may be considered to arise from (anti)M-branes wrapping around the internal directions in the (Wick-rotated) skew-whiffed M2-brane background (as the resulting theory is for anti-M2-branes), thus realizing the modes after swapping the three fundamental representations , , and of . Taking the backreaction on the external and internal spaces, we obtain the massless and massive modes, corresponding to exactly marginal and marginally irrelevant deformations on the boundary CFT , respectively. Subsequently, we obtain a closed solution for the bulk equation and compute its correction with respect to the background action. Next, considering the Higgs-like (breathing) mode , having all supersymmetries as well as parity and scale-invariance broken, solving the associated bulk equation with mathematical methods, specifically the Adomian decomposition method, and analyzing the behavior near the boundary of the solutions, we realize the boundary duals in the -singlet sectors of the ABJM model. Then, introducing the new dual deformation operators made of bi-fundamental scalars, fermions, and gauge fields, we obtain the -invariant solutions as small instantons on a three-sphere with the radius at infinity, which correspond to collapsing bulk bubbles leading to big-crunch singularities.

Exploring the Quantum Spectral Curve for AdS3/CFT2

Despite the rich and fruitful history of the integrability approach to string theory on the AdS3 × S3 × T4 background, it has not been possible to extract many concrete predictions from integrability, except in a strict asymptotic regime of large quantum numbers, due to the severity of wrapping effects. The situation changed radically with two independent and identical proposals for the Quantum Spectral Curve (QSC) for this system in a background of pure Ramond-Ramond flux. In other integrable superstring backgrounds there is compelling evidence that this formulation captures all wrapping effects exactly and describes the full planar spectrum. This great success motivates us to study the new proposed QSC and develop methods to extract from it concrete predictions for spectral data. The AdS3 × S3 × T4 case presents a significant novel feature and challenge compared to its higher-dimensional analogues — massless modes. It has been conjectured that these manifest themselves in a new property of this QSC: the non-quadratic nature of the branch-cut singularities of the QSC Q-functions. This feature implies new technical challenges in solving the QSC equations as compared to the well-studied case of 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 SYM. In this paper we resolve these difficulties and obtain the first ever predictions for unprotected string excitations in the planar limit with finite quantum numbers and RR flux. We explain how to extract a systematic expansion around the analogue of the weak ’t Hooft coupling limit 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 SYM and also obtain high-precision numerical results. These concrete data and others obtainable from the QSC could help to identify the so-far mysterious dual CFT.

Probability measures of fermions on branes

In our research, we explore the impact of a geometric non-minimal coupling between fermions and curvature scalars on the positioning of fermions within a brane structure. Our investigation encompasses massless fermionic modes and massive modes, revealing that specifically fermionic modes with left chirality are situated within the brane. This insight allows us to gain a more direct understanding of how the system’s geometry influences the placement of fermion fields on the brane. To delve deeper into the precise localization of massless fermionic modes, we employ entropic information measurements. By varying the parameters that govern the curvature scalars, we observe the ability to adjust the localization of these fermionic modes on the brane. Importantly, the BBM uncertainty relation remains satisfied in all scenarios, particularly for f1,2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{1,2,3}$$\\end{document}. We leverage the Shannon entropy as a highly effective metric to yield accurate results regarding the positioning of massless fermionic modes within our model. In the case of massive fermionic modes, we utilize relative probability analysis to pinpoint the resonant modes, and we identify the existence of these resonant modes in both f1,2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{1,2,3}$$\\end{document} cases. Ultimately, we ascertain that these parameters influence the placement of resonant modes by increasing the amplitude of the massive modes in the core of the brane.

S-matrix on effective string and compactified membrane

Expanding Nambu–Goto action near infinitely long string vacuum one can compute scattering amplitudes of 2d massless fields representing transverse string coordinates. As was shown in (Dubovsky et al 2012 J. High Energy Phys. JHEP09(2012)044), the resulting S-matrix is integrable (provided appropriate local counterterms are added), in agreement with known free string spectrum and also with an interpretation of the static-gauge NG action as a deformation of a free massless theory. We consider a generalization of this computation to the case of a membrane, expanding its 3d action near an infinite membrane vacuum that has cylindrical shape (we refer to such membrane as ‘compactified’). Representing 3d fields as Fourier series in S 1 coordinate we get an effective 2d model in which the massless string modes are coupled to an infinite KK tower of massive 2d modes. We find that the resulting 2d S-matrix is not integrable already at the tree level. We also compute 1-loop scattering amplitude of massless string modes with all compactified membrane modes propagating in the loop. The result is UV finite and is a non-trivial function of the kinematic variables. In the large momentum limit or when the radius of S 1 is taken to infinity we recover the expression for the 1-loop scattering amplitude of the uncompactified membrane. We also consider a 2d model which is the deformation to the free theory with the same massless plus infinite massive tower of modes. The corresponding 2d S-matrix is found, as expected, to be integrable. Contribution to the special issue of Journal of Physics A: ‘Fields, Gravity, Strings and Beyond: In Memory of Stanley Deser’

Study on Kalb–Ramond field localization in f(T) gravity theory with a noncanonical scalar field

In this paper, we investigate the localization of five-dimensional tensor gauge fields called Kalb–Ramond fields in the modified teleparallel braneworld models. The aforementioned branes are generated by gravity coupled to a real scalar field with nonstandard kinetic terms. For two specific forms of the noncanonical expressions, background scalar field solutions are particularly discussed in the presence of different forms of [Formula: see text] gravity. By applying nonminimal coupling functions in the tensor gauge field action, it is shown that massless zero modes of Kalb–Ramond gauge fields can be localized on the [Formula: see text] branes with noncanonical scalar fields. We also find that potentials of Kalb–Ramond massive modes are volcano-like regarding the equation of motion in the supersymmetric quantum mechanic scenario. Furthermore, the effects of parameters that control the deviation of the usual teleparallel theory are considered on the massless Kaluza–Klein mode and effective potential.

Quasinormal modes and optical properties of 4-D black holes in Einstein Power-Yang–Mills gravity

This paper explores the impact of the Yang–Mills charge parameter and the exponent term on a 4D black hole solution in the Einstein Power-Yang–Mills theory. Through an investigation of the massless scalar quasinormal mode spectrum, black hole shadow, and emission rate, we have determined that the effects of these two parameters are opposite. Specifically, the Yang–Mills charge parameter causes an increase in the real quasinormal frequencies with a correspondingly smaller damping rate. It also results in a smaller black hole shadow and a lower evaporation rate.

Non-supersymmetric vacua and self-adjoint extensions

Internal intervals spanned by finite ranges of a conformal coordinate z and terminating at a pair of singularities are a common feature of many string compactifications with broken supersymmetry. The squared masses emerging in lower-dimensional Minkowski spaces are then eigenvalues of Schrödinger-like operators, whose potentials have double poles at the ends of the intervals. For one-component systems, the possible self-adjoint extensions of Schrödinger operators are described by points in AdS3 × S1, and those corresponding to independent boundary conditions at the ends of the intervals by points on the boundary of AdS3. The perturbative stability of compactifications to Minkowski space time depends, in general, on these choices of self-adjoint extensions. We apply this setup to the orientifold vacua driven by the “tadpole potential” V=T {e}^{frac{3}{2}phi } and find, in nine dimensions, a massive scalar spectrum, a unique choice of boundary conditions with stable tensor modes and a massless graviton, and a wide range of choices leading to massless and/or massive vector modes.

Chiral perturbative analysis for an almost massless neutrino in the type-I seesaw mechanism

In this paper, we perform chiral perturbative analysis of an approximate lepton number symmetry associated with a sufficiently light neutrino in the type-I seesaw mechanism. For the Dirac mass matrix mD=(A,B,C), linearly independent components of C from A and B are treated as symmetry-breaking parameters. A deviation in the eigenvector of the massless mode δu occurs in the first-order perturbation and the lightest mass m1or 3∝det⁡mD2/M3 emerges in the second-order. By solving the perturbation theory, we obtained specific expressions of δu and m1or 3. As a result, two complex parameters in mD are bounded to some extent from the eigenvector. These constraints are associated with the chiral symmetry and are not susceptible to renormalization.