Gravitational Anomalies Research Articles

Hint to supersymmetry from the GR vacuum

The S-matrix formulation of gravity suggests that the θ-vacuum structure must not be sustained by the theory. We point out that, when applied to the vacuum of general relativity, this criterion hints to supersymmetry. The topological susceptibility of gravitational vacuum induced by Eguchi-Hanson instantons can be eliminated neither by spin-1/2 fermions nor by an axion coupled via them since such fermions do not provide instanton zero modes. Instead, the job is done by a spin-3/2 fermion, hence realizing a local supersymmetry. This scenario also necessitates the spontaneous breaking of supersymmetry and predicts the existence of axion of R symmetry which gets mass exclusively from the gravitational instantons. The R axion can be a viable dark matter candidate. Matching between the index and the anomaly imposes a constraint that spin-1/2 fermions should not contribute to the chiral gravitational anomaly. Published by the American Physical Society 2024

Measurements of the Low-acceleration Gravitational Anomaly from the Normalized Velocity Profile of Gaia Wide Binary Stars and Statistical Testing of Newtonian and Milgromian Theories

Low-acceleration gravitational anomaly is investigated with a new method of exploiting the normalized velocity profile v˜≡vp/vc of wide binary stars as a function of the normalized sky-projected radius s/r M, where v p is the sky-projected relative velocity between the pair, v c is the Newtonian circular velocity at the sky-projected separation s, and r M is the MOND radius. With a Monte Carlo method, Gaia observed binaries and their virtual Newtonian counterparts are probabilistically distributed on the s/r M versus v˜ plane, and a logarithmic velocity ratio parameter Γ is measured in the bins of s/r M. With three samples of binaries covering a broad range in size, data quality, and implied fraction of hierarchical systems including a new sample of 6389 binaries selected with accurate distances and radial velocities, I find a unanimous systematic variation from the Newtonian flat line. With Γ = 0 at s/r M ≲ 0.15 or s ≲ 1 kau, I get Γ = 0.068 ± 0.015 (stat) −0.015+0.024 (syst) for s/r M ≳ 0.7 or s ≳ 5 kau. The gravitational anomaly (i.e., acceleration boost) factor given by γ g = 102Γ is measured to be γg=1.37−0.09+0.10 (stat) −0.09+0.16 (syst). With a reduced χ 2 test of Newtonian and Milgromian nonrelativistic theories, I find that Newtonian gravity is ruled out at 5.8σ ( χν2=9.4 ) by the new sample (and 9.2σ by the largest sample used). The Milgromian AQUAL theory is acceptable with 0.7≲χν2≲3.1 . These results agree well with earlier results with the “acceleration-plane analysis” for a variety of samples and the “stacked velocity profile analysis” for a pure binary sample.

Ward identities in a two-dimensional gravitational model: anomalous amplitude revisited using a completely regularization-independent mathematical strategy

We present a detailed investigation of the anomalous gravitational amplitude in a simple two-dimensional model with Weyl fermions. We employ a mathematical strategy that completely avoids any regularization prescription for handling divergent perturbative amplitudes. This strategy relies solely on the validity of the linearity of the integration operation and avoids modifying the amplitudes during intermediate calculations, unlike studies using regularization methods. Additionally, we adopt arbitrary routings for internal loop momenta, representing the most general analysis scenario. As expected, we show that surface terms play a crucial role in both preserving the symmetry properties of the amplitude and ensuring the mathematical consistency of the results. Notably, our final perturbative amplitude can be converted into the form obtained using any specific regularization prescription. We consider three common scenarios, one of which recovers the traditional results for gravitational anomalies. However, we demonstrate that this scenario inevitably breaks the linearity of integration, leading to an undesirable mathematical situation. This clean and transparent conclusion, enabled by the general nature of our strategy, would not be apparent in similar studies using regularization techniques.

Unscented Schmidt-Kalman filter on Lie groups with application to spacecraft attitude estimation

This paper addresses the estimation problem of nonlinear systems evolving on Lie groups with unknown parameters. More precisely, some parameters in the equations of motion or sensor measurements are unknown, such as gravitational anomalies and measurement biases, and are infeasible to estimate with available observations. The unscented Schmidt-Kalman filter (USKF) approach in Euclidean space is incorporated with exponential maps from Lie algebra to Lie groups, to develop USKF algorithms on Lie groups. Two types of USKFs are derived, respectively, from left-invariant and right-invariant state estimation errors. The two USKFs, not only account for the effect of unknown parameters but also provide estimates preserving the geometry of state manifold. They are advantageous over the extended Schmidt-Kalman filter for nonlinear systems in the sense of avoiding the computation of Jacobian and achieving higher or comparable estimation accuracy depending on the magnitude of parameters uncertainties. The proposed method is then applied to a spacecraft attitude estimation problem based on quaternion representation, where the magnitude of the gyroscope bias noise is unknown. Simulations are conducted to illustrate the effectiveness of the proposed algorithms in comparison with other methods.

Neotectonic structures of the Eastern Taimyr and their relationship with gravitational anomalies and seismicity

The study of the newest structures of the east of the Taimyr Peninsula, expressed in relief, was carried out using the structural and geomorphological method, which allows to identify the latest deformations, which were compared with the features of the gravitational field and its transformants. A good correspondence between gravitational anomalies and the magnitude of erosion uplifts is shown, and the confinement of the selected blocks and their boundaries to the peculiarities of the transformant field is established. The zones of seismicity within the Eastern Taimyr and adjacent territories tend to faults active in the Cenozoic period, as well as to an elongated zone of contrasting values of gravitational anomalies and their transformants of the strike zone.

Axion‐Like Interactions and CFT in Topological Matter, Anomaly Sum Rules and the Faraday Effect

AbstractFundamental aspects of chiral anomaly‐driven interactions in conformal field theory (CFT) in four spacetime dimensions are discussed. These interactions find application in very general contexts, from early universe plasma to topological condensed matter. The key shared characteristics of these interactions are outlined, specifically addressing the case of chiral anomalies, both for vector currents and gravitons. In the case of topological materials, the gravitational chiral anomaly is generated by thermal gradients via the (Tolman–Ehrenfest) Luttinger relation. In the CFT framework, a nonlocal effective action, derived through perturbation theory, indicates that the interaction is mediated by excitation in the form of an anomaly pole, which appears in the conformal limit of the vertex. To illustrate this, it is demonstrated how conformal Ward identities (CWIs) in momentum space allow to reconstruct the entire chiral anomaly interaction in its longitudinal and transverse sectors just by inclusion of a pole in the longitudinal sector. Both sectors are coupled in amplitudes with an intermediate chiral fermion or a bilinear Chern–Simons current with intermediate photons. In the presence of fermion mass corrections, the pole transforms into a cut, but the absorption amplitude in the axial‐vector channel satisfies mass‐independent sum rules related to the anomaly in any chiral interaction. The detection of an axion‐like/quasiparticle in these materials may rely on a combined investigation of these sum rules, along with the measurement of the angle of rotation of the plane of polarization of incident light when subjected to a chiral perturbation. This phenomenon serves as an analog of a similar one in ordinary axion physics, in the presence of an axion‐like condensate, which is rederived using axion electrodynamics.

A critical review of recent Gaia wide binary gravity tests

ABSTRACT Over the last couple of years, the appearance of the third data release from the Gaia satellite has triggered various wide binary low acceleration gravity tests. Wide binaries with typical total masses $\approx 1.0 - 1.6\,\mathrm{ M}_{\odot }$ and separations above a few thousand au probe the low acceleration $a \lesssim a_{0}$ regime, where at galactic and larger scales gravitational anomalies typically attributed to the presence of an as yet undetected dark matter component appear, where $a_{0} \approx 1.2\times 10^{-10}$ m s$^{-2}$ is the acceleration scale of Modified Newtonian Dynamics (MOND). Thus, studies of the relative velocities and separations on the plane of the sky, $v_{2\mathrm{ D}}$ and $s_{2\mathrm{ D}}$, respectively, of wide binary stars extending to separations above a few kau, provide an independent approach on the empirical study of gravity in the interesting $a \lesssim a_{0}$ acceleration range. Two independent groups, through complementary approaches, have obtained evidence for a departure from Newtonian predictions in the low acceleration regime, in consistency with MOND expectations for wide binary orbits in the Solar Neighbourhood. Two other groups however, have instead reported results showing a clear preference for Newtonian gravity over various MOND alternatives tested, over the same low acceleration regime. We here take a critical look at the various studies in question, from sample selection to statistical treatment of the wide binary relative velocities obtained. We discover a couple of critical problems in the formal design and statistical implementation shared by the two latter groups, and show explicitly how these yield biased conclusions.

Nontriviality of dynamical Chern-Simons gravity and the standard model

Given the growing interest in gravitational-wave and cosmological parity-violating effects in dynamical Chern-Simons (dCS) gravity, it is crucial to investigate whether the scalar-gravitational Pontryagin term in dCS gravity persists when formulated in the context of the U(1)B−L anomaly in the standard model (SM). In particular, it has been argued that dCS gravity can be reduced to Einstein gravity after “rotating away” the gravitational-Pontryagin coupling into the phase of the Weinberg operator—analogous to the rotation of the axion zero mode into the quark mass matrix. We find that dCS gravity is nontrivial if the scalar field ϕ has significant spacetime dependence from dynamics. We provide a comprehensive consideration of the dCS classical and quantum symmetries relevant for embedding a dCS sector in the SM. We find that, because of the baryon/lepton number chiral gravitational anomaly, the scalar-Pontryagin term cannot be absorbed by a field redefinition. Assuming a minimal extension of the SM, we also find that a coupling of the dCS scalar with right-handed neutrinos induces both the scalar-Pontryagin coupling and an axionlike phase in the dimension-five Weinberg operator. We comment on the issue of gauging the U(1)B−L, the observational effects with these two operators present for upcoming experiments, and the origin of dCS gravity in string theory. Published by the American Physical Society 2024

Gravitational chiral anomaly at finite temperature and density

We investigate the gravitational anomaly vertex ⟨TTJ5⟩ (graviton—graviton—axial current) under conditions of finite density and temperature. Through a direct analysis of perturbative contributions, we demonstrate that neither finite temperature nor finite fermion density affects the gravitational chiral anomaly. These results find application in several contexts, from topological materials to the early Universe plasma. They affect the decay of any axion or axionlike particle into gravitational waves, in very dense and hot environments. Published by the American Physical Society 2024

Axial anomalies of maximally supersymmetric tensor theories

We revisit anomalies of (4, 0) and (3, 1) maximally supersymmetric tensor theories in d = 6. A (4, 0) on-shell tensor multiplet descends to that of the d = 5 maximal supergravity upon a dimensional reduction, hypothesized to offer a strong-coupled UV completion of the latter in the same sense of (2, 0) theories as the UV completion of d = 5 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} = 2 pure Yang-Mills. The gravitational anomalies, found to be nonvanishing, had been computed, although its relevance in the absence of the d = 6 metric is not obvious. We perform a comprehensive anomaly computation for (4, 0) and (3, 1) tensor supermultiplets, respectively, for Sp(4) and Sp(3) × Sp(1) R-symmetry anomalies and the mixed R-gravitational anomaly thereof, and find that anomalies involving R-symmetries cancel out identically. We close with questions on how to address the anomaly in this class of theories with no general covariance.

Development of Earth Gravity Models in A Sustainable Environment: An Overview of Nigeria’s Ecosystem

The evolution of Earth gravity models in Nigeria's ecological context is essential for advancing sustainable environmental stewardship. These models serve as crucial tools to understand the geological intricacies and environmental dynamics across Nigeria's diverse ecosystems. This article obtained data from previous existing data to emphasizes the significance of sustainable development, technological innovation, and the integration of sustainability principles into Earth gravity modeling efforts. The gravitational variations observed across Nigeria's ecosystems highlight the diverse geological features influencing gravitational anomalies. For instance, forests with dense vegetation exhibit gravitational variations ranging from -5.2 to -2.8 mGal, while coastal areas experiencing erosion and sea level rise show variations from -1.8 to 1.0 mGal. The article explores both advancements and challenges in developing Earth gravity models within Nigeria's unique environmental landscape, emphasizing the intersection of technology and sustainability. By leveraging advanced technologies and interdisciplinary methodologies, Earth gravity models contribute significantly to understanding the gravitational forces shaping the planet's surface and subsurface. Understanding the methodology behind Earth gravity models in a sustainable environment is crucial for effective environmental management and resource conservation, providing valuable tools for preserving Nigeria's diverse ecosystems for future generations. Through this integrated approach, Earth gravity models pave the way for enhanced environmental monitoring, land-use planning, and conservation strategies tailored to Nigeria's specific ecological challenges and opportunities.

Gravity-gauge anomaly constraints on the energy-momentum tensor

We derive constraints on the four dimensional energy-momentum tensor from gravitational and gauge anomalies. Our work can be considered an extension of Duff’s analysis [1] to include parity-odd terms and explicit symmetry breaking. The constraints imply the absence of the parity-odd RR~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ R\\overset{\\sim }{R} $$\\end{document} and FF~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ F\\overset{\\sim }{F} $$\\end{document} terms, for theories whose symmetries are compatible with dimensional regularisation, in a model-independent way. Remarkably, even in the case of explicit symmetry breaking the □R-anomaly is found to be finite and unambiguous after applying the symmetry constraints. We compute mixed gravity-gauge anomalies at leading order and deduce phenomenological consequences for vector bosons associated with global chiral symmetries.

The vertical accuracy improvement method considering gravitational anomaly for SINS/GNSS

Vertical information (vertical velocity and altitude) is important in three-dimensional navigation. In order to improve the vertical accuracy of strapdown inertial navigation system/global navigation satellite system integrated navigation (SINS/GNSS) while reducing costs, firstly, the propagation laws of vertical error sources in two types of SINS/GNSS (vertical velocity set to 0 and not set to 0) are systematically analyzed. Furthermore, a vertical accuracy improvement method considering the gravitational anomaly is proposed. In this method, the gravitational anomaly is considered as one of the vertical error sources. Then, the processing method of error sources in integrated navigation is referenced, and two processing modes of gravitational anomaly are designed. The first method is to represent the gravitational anomaly as one of the system states of SINS/GNSS. The number of dimensions for the system is expanded from 15 to 16. The corresponding mathematical model is derived to ‘absorb’ the vertical errors caused by the gravitational anomaly. The second is to represent the gravitational anomaly as one of the vertical system noises. Thereby, the Kalman filter is adjusted in real time using the above adaptive method to improve the accuracy of the estimated state. The corresponding errors are then suppressed. Field experiments show that both modes of the proposed method can effectively improve the vertical accuracy.

The SU(3)C × SU(3)L × U(1)X (331) Model: Addressing the Fermion Families Problem within Horizontal Anomalies Cancellation.

One of the most important and unanswered problems in particle physics is the origin of the three generations of quarks and leptons. The Standard Model does not provide any hint regarding its sequential charge assignments, which remain a fundamental mystery of Nature. One possible solution of the puzzle is to look for charge assignments, in a given gauge theory, that are inter-generational, by employing the cancellation of the gravitational and gauge anomalies horizontally. The 331 model, based on an SU(3)C×SU(3)L×U(1)X does this in an economical way and defines a possible extension of the Standard Model, where the number of families has necessarily to be three. We review the model in Pisano, Pleitez, and Frampton's formulation, which predicts the existence of bileptons. Another characteristics of the model is to unify the SU(3)C×SU(2)L×U(1)X into the 331 symmetry at a scale that is in the TeV range. Expressions of the scalar mass eigenstates and of the renormalization group equations of the model are also presented.

New anomaly free supergravities in six dimensions

An extended search for anomaly free matter coupled N = (1, 0) supergravity in six dimension is carried out by two different methods which we refer to as the graphical and rank methods. In the graphical method the anomaly free models are built from single gauge group models, called nodes, which can only have gravitational anomalies. We search for anomaly free theories with gauge groups G1 × … × Gn with n = 1, 2, … (any number of factors) and G1 × … × Gn × U(1)R where n = 1, 2, 3 and U(1)R is the R-symmetry group. While we primarily consider models with the tensor multiplet number nT = 1, we also provide some results for nT ≠ 1 with an unconstrained number of charged hypermultiplets. We find a large number of ungauged anomaly free theories. However, in the case of R-symmetry gauged models with nT = 1, in addition to the three known anomaly free theories with G1 × G2 × U(1)R type symmetry, we find only six new remarkably anomaly free models with symmetry groups of the form G1 × G2 × G3 × U(1)R. In the case of nT = 1 and ungauged models, excluding low rank group factors and considering only low lying representations, we find all anomaly free theories. Remarkably, the number of group factors does not exceed four in this class. The proof of completeness in this case relies on a bound which we establish for a parameter characterizing the difference between the number of non-singlet hypermultiplets and the dimension of the gauge group.

On the frozen F-theory landscape

We study 6d \\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, 0) supergravity theories arising in the frozen phase of F-theory. For each of the known global models, we construct an F-theory compactification in the unfrozen phase with an identical non-abelian gauge algebra and massless matter content. Two such low energy effective theories are then distinguished through gauge enhancements in moduli space. We study potentially new global models obtained via compact embeddings of a plethora of 6d \\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, 0) superconformal field theories and little string theories constructed using frozen 7-branes. In some cases, these provably do not exist, and in other cases, we explicitly construct a compact embedding, yielding 6d supergravity theories with new massless spectra. Finally, by using gravitational anomaly cancellation, we conjecture the existence of localized neutral hypermultiplets along frozen 7-brane loci.

Higher-group symmetry of (3+1)D fermionic $\mathbb{Z}_2$ gauge theory: Logical CCZ, CS, and T gates from higher symmetry

It has recently been understood that the complete global symmetry of finite group topological gauge theories contains the structure of a higher-group. Here we study the higher-group structure in (3+1)D \mathbb{Z}_2ℤ2 gauge theory with an emergent fermion, and point out that pumping chiral p+ipp+ip topological states gives rise to a \mathbb{Z}_{8}ℤ8 0-form symmetry with mixed gravitational anomaly. This ordinary symmetry mixes with the other higher symmetries to form a 3-group structure, which we examine in detail. We then show that in the context of stabilizer quantum codes, one can obtain logical CCZ and CS gates by placing the code on a discretization of T^3T3 (3-torus) and T^2 \rtimes_{C_2} S^1T2⋊C2S1 (2-torus bundle over the circle) respectively, and pumping p+ipp+ip states. Our considerations also imply the possibility of a logical TT gate by placing the code on \mathbb{RP}^3ℝℙ3 and pumping a p+ipp+ip topological state.

Hydrodynamical dual of the gravitational axial anomaly and the cosmological constant

We construct the hydrodynamic expansion for a rotating and accelerated medium in a curved space-time, and establish the relationship between the currents generated by the cosmological constant and the acceleration. Then we consider the more general case with a nonzero Weyl tensor, and show the duality between the current in flat space-time and the gravitational axial anomaly. This generalizes the previous derivation to the case with a nonzero Ricci tensor. Published by the American Physical Society 2024

Anomaly constraints for heterotic strings and supergravity in six dimensions

The landscape of six-dimensional supergravities is dramatically constrained by the cancellation of gauge and gravitational anomalies, but the full extent of its implications has not been uncovered. We explore the cancellation of global anomalies of the Dai-Freed type in this setting with abelian and simply laced gauge groups, finding novel constraints. In particular, we exclude arbitrarily large abelian charges in an infinite family of theories for certain types of quadratic refinements, including a specific one defined in the literature. We also show that the Gepner orientifold with no tensor multiplets is anomaly-free for a different choice, as well as a number of heterotic models with and without spacetime supersymmetry in six dimensions. The latter analysis extends previous results in ten dimensions to some lower-dimensional settings in the heterotic landscape.

Anomalous Luttinger equivalence between temperature and curved spacetime: From black holes to thermal quenches

Building on the idea of Tolman and Ehrenfest that heat has weight, Luttinger established a deep connection between gravitational fields and thermal transport. However, this relation does not include anomalous quantum fluctuations that become paramount in strongly curved spacetime. In this work, we revisit the celebrated Tolman-Ehrenfest and Luttinger relations and show how to incorporate the quantum energy scales associated with these fluctuations, captured by gravitational anomalies of quantum field theories. We point out that such anomalous fluctuations naturally occur in the quantum atmosphere of a black hole. Our results reveal that analogous fluctuations are also observable in thermal conductors in flat-space time provided local temperature varies strongly. As a consequence, we establish that the gravitational anomalies manifest themselves naturally in non-linear thermal response of a quantum wire. In addition, we propose a systematic way to identify thermal analogues of black hole’s anomalous quantum fluctuations associated to gravitational anomalies. We identify their signatures in propagating energy waves following a thermal quench, as well as in the energy density of heating Floquet states induced by repeated thermal quenches.