Anomalous Theory Research Articles

Towards non-invertible anomalies from generalized Ising models

We present a general approach to the bulk-boundary correspondence of noninvertible topological phases, including both topological and fracton orders. This is achieved by a novel bulk construction protocol where solvable (d+1)(d+1)-dimensional bulk models with noninvertible topology are constructed from the so-called generalized Ising (GI) models in dd dimensions. The GI models can then terminate on the boundaries of the bulk models. The construction generates abundant examples, including not only prototype ones such as \mathbb{Z}_2ℤ2 toric code models in any dimensions no less than two, and the X-cube fracton model, but also more diverse ones such as the \mathbb{Z}_2x \mathbb{Z}_2ℤ2xℤ2 topological order, the 4d \mathbb{Z}_2ℤ2 topological order with pure-loop excitations, etc. The boundary of the solvable model is potentially anomalous and corresponds to precisely only sectors of the GI model that host certain total symmetry charges and/or satisfy certain boundary conditions. We derive a concrete condition for such bulk-boundary correspondence. The condition is violated only when the bulk model is either trivial or fracton ordered. A generalized notion of Kramers-Wannier duality plays an important role in the construction. Also, utilizing the duality, we find an example where a single anomalous theory can be realized on the boundaries of two distinct bulk fracton models, a phenomenon not expected in the case of topological orders. More generally, topological orders may also be generated starting with lattice models beyond the GI models, such as those with symmetry protected topological orders, through a variant bulk construction, which we provide in an appendix.

Research on the structure of cosmic-ray electron and positron fluxes in GeV–TeV energy range

The positron–electron fluxes detected by AMS02, CALET, DAMPE and Fermi-LAT have shown their complex structure which deviated from a single power-law, and the results of DAMPE and Fermi-LAT are obviously higher than those of AMS02 and CALET in 100[Formula: see text]GeV–1[Formula: see text]TeV range. We point out that the complex positron–electron flux structures can be attributed to two sources with a natural background, and the difference between the two groups of data can be explained in an anomalous bremsstrahlung theory.

Global anomalies on the Hilbert space

We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert space are identified with the distinct cohomology “layers” that appear in the classification of anomalies in terms of cobordism groups. We illustrate the manifestation of the layers in the Hilbert for a variety of anomalous symmetries and spacetime dimensions, including time-reversal symmetry, and both in systems of fermions and in anomalous topological quantum field theories (TQFTs) in 2 + 1d. We argue that anomalies can imply an exact bose-fermi degeneracy in the Hilbert space, thus revealing a supersymmetric spectrum of states; we provide a sharp characterization of when this phenomenon occurs and give nontrivial examples in various dimensions, including in strongly coupled QFTs. Unraveling the anomalies of TQFTs leads us to develop the construction of the Hilbert spaces, the action of operators and the modular data in spin TQFTs, material that can be read on its own.

Anomalies and Bosonization

Recently, general methods of bosonization beyond 1+1 dimensions have been developed. In this article, we review these bosonizations and extend them to systems with boundary. Of particular interest is the case when the bulk theory is a G-symmetry protected topological phase and the boundary theory has a G ’t Hooft anomaly. We discuss how, when the anomaly is not realizable in a bosonic system, the G symmetry algebra becomes modified in the bosonization of the anomalous theory. This gives us a useful tool for understanding anomalies of fermionic systems, since there is no way to compute a boundary gauge variation of the anomaly polynomial, as one does for anomalies of bosonic systems. We take the chiral anomalies in 1+1D as case studies and comment on our expectations for parity/time reversal anomalies in 2+1D. We also provide a derivation of new constraints in SPT phases with domain defects decorated by $$p+ip$$ superconductors and Kitaev strings, which is necessary to understand the bosonized symmetry algebras which appear.

Wettability evolution of different nanostructured cobalt films based on electrodeposition

The wettability evolution of eight different types of nanostructured cobalt films is investigated using galvanostatic electrodeposition. The morphology, which evolves from a plump, pea-like structure to cone, pyramid, shell, fluffy cone, fluffy shell and flower structures can be controlled by changing the anion type in the electrolyte or the deposition current density. A growth mechanism is proposed based on cathodic anomalous absorption theory, which explains both the influence of the anion type on the surface structure and the current-dependent morphology evolution. The contact angle and sliding angle of all films are measured, and fractions of water drop contact area with the surrounding air are calculated to illustrate the roughness induced wettability. The hierarchical (nano and micro) structures exhibit eminent superhydrophobicity compared with single dimensional surfaces, indicating this as an effective way to prevent transition from Cassie–Baxter mode to Wenzel mode.

Ordinary matter, dark matter, and dark energy on normal Zeeman space-times

Zeeman space-times are new, relativistic, and operator based Hamiltonian models representing multi-particle systems. They are established on Lorentzian pseudo Riemannian manifolds whose Laplacian immediately appears in the form of original quantum physical wave operators. In classical quantum theory they emerge, differently, from the Hamilton formalism and the correspondence principle. Nonetheless, this new model does not just reiterate the well known conceptions but holds the key to solving open problems of quantum theory. Most remarkably, it represents the dark matter, dark energy, and ordinary matter by the same ratios how they show up in experiments. Another remarkable agreement with reality is that the ordinary matter appears to be non-expanding and is described in consent with observations. The theory also explains gravitation, moreover, the Hamilton operators of all energy and matter formations, together with their physical properties, are solely derived from the Laplacian of the Zeeman space-time. By this reason, it is called Monistic Wave Laplacian which symbolizes an all-comprehensive unification of all matter and energy formations. This paper only outlines the normal case where the particles do not have proper spin but just angular momentum. The complete anomalous theory is detailed in [Sz2, Sz3, Sz4, Sz5, Sz6, Sz7].

Boundary Conditions for Topological Quantum Field Theories, Anomalies and Projective Modular Functors

We study boundary conditions for extended topological quantum field theories (TQFTs) and their relation to topological anomalies. We introduce the notion of TQFTs with moduli level $m$, and describe extended anomalous theories as natural transformations of invertible field theories of this type. We show how in such a framework anomalous theories give rise naturally to homotopy fixed points for $n$-characters on $\infty$-groups. By using dimensional reduction on manifolds with boundaries, we show how boundary conditions for $n+1$-dimensional TQFTs produce $n$-dimensional anomalous field theories. Finally, we analyse the case of fully extended TQFTs, and show that any fully extended anomalous theory produces a suitable boundary condition for the anomaly field theory.

Hamiltonian Anomalies from Extended Field Theories

We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.

Influence of anomalous particle diffusion on the current system formation and coherence of Pi2 geomagnetic pulsation local ionospheric sources

The coherence conditions for local ionospheric sources of Pi2 high-latitude geomagnetic pulsations in the 6–8 mHz frequency band were studied with a method for representing their component spatial distributions by vertical magnetic dipole field integrals over random walk trajectories in the ionospheric horizontal plane. High-quality representations are reached when the field intensity is proportional to a self-intersection density that has spatial and time walk trajectory discontinuities. According to anomalous diffusion theory, the trajectory of the subordinate Levy process is characterized by the stabilization of turning points grouped near pulsation local ionospheric sources. This makes it possible to simulate disturbances of the Pi2 high-latitude pulsation field by a uniform motion along the Hall ionospheric source Levy trajectories with short-term pulsed current switching on-off. A coherent redistribution of the Pi2 local ionospheric source intensity and several observed specific features in the source field distribution dynamics are explained by the independent processes of local field-aligned current formation and intensification-weakening of pulsations caused by the current carrier shift relative to wandering Levy turning points and a stationary observer.

Theory of asymmetric electrochemical stochastic diffusion

Strict analysis of electrochemical strochastic diffusion due to asymmetric Brownian motion of electric charge in an equilibrium electrochemical ac circuit containing double electric layer capacitance and noisy Faradaic resistance is carried out. Cumulant analogs (for 3rd and 5th order correlations) of the Einstein formula are obtained. It is proved that equilibrium asymmetric (nongauss) stochastic diffusion is in agreement with the central limiting theorem of the probability theory. The Hurst exponent was found in the case of the nongauss components of the process of equilibrium stochastic diffusion. Apart from electrochemistry, the performed stochastic analysis of equilibrium electrochemical nongauss diffusion is also of general theoretical interest, including its application in the stochastic theory of asymmetric anomalous transport and strict theory of fluctuations at large deviations from equilibrium.

Anomalous U(1) models in four and five dimensions and their anomaly poles

We analyze the role played by anomaly poles in an anomalous gauge theory by discussing their signature in the corresponding off-shell effective action. The origin of these contributions, in the most general kinematical case, is elucidated by performing a complete analysis of the anomaly vertex at perturbative level. We use two independent (but equivalent) representations: the Rosenberg representation and the longitudinal/transverse (L/T) parameterization, used in recent studies of g−2 of the muon and in the proof of non-renormalization theorems of the anomaly vertex. The poles extracted from the L/T parameterization do not couple in the infrared for generic anomalous vertices, as in Rosenberg, but we show that they are responsible for the violations of unitarity in the UV region, using a class of pole-dominated amplitudes. We conclude that consistent formulations of anomalous models require necessarily the cancellation of these polar contributions. Establishing the UV significance of these terms provides a natural bridge between the anomalous effective action and its completion by a nonlocal theory. Some additional difficulties with unitarity of the mechanism of inflow in extra dimensional models with an anomalous theory on the brane, due to the presence of anomaly poles, are also pointed out.

Magnetic and Transport Properties of Mn-Si Films Synthesized on 4H-SiC(0001) Substrates

We report a systematic study of the thickness dependence of magnetic properties in carbon-incorporated Mn-Si films synthesized on a 4H-SiC(0001) homoepitaxial wafer by molecular beam epitaxy (MBE) and an annealing method. Magnetization characteristics reveal a dual-phase characteristic in films with decreasing thickness. The anomalous Hall effect has been observed in the thicker film; however, the observed temperature dependence cannot be explained by traditional anomalous Hall effect theory. The temperature dependent resisitivity indicates the film has a metallic behavior.

High-accuracy calculations of term energies and lifetimes of silicon-like ions with nuclear charges Z = 24–30

Term energies of the ground and 26 lowest excited levels arising from the 3s23p2, 3s3p3 and 3s23p3d configurations in silicon-like ions with nuclear charges Z = 24–30 are evaluated to high accuracy in relativistic multireference many-body perturbation theory calculations. Theory deviates from experiment on the order of 0.01% for the majority, and by less than 0.2% for all but 13, of the experimentally identified energy levels. Anomalous theory–experiment deviations along the isoelectronic sequence for six excited levels clearly indicate that they have been misidentified, among them the solar lines at 237.61 Å and 259.963 Å. New identifications for the misidentified levels are given based on theoretical wavelengths and lifetimes. Hitherto unidentified 3s23p3d 3Fo2,3,4 decay lines along the isoelectronic sequence are predicted to well within 0.1 Å accuracy. Calculated lifetimes of the odd-parity 3s23p3d 3Fo3 state in silicon-like ions agree reasonably well with experiment, Co13+ being the exception.

QED from six-dimensional vortex and gauge anomalies

Starting from an anomaly-free Abelian Higgs model coupled to gravity in a 6-dimensional space-time we construct an effective four-dimensional theory of charged fermions interacting with U(1) Abelian gauge field and gravity, both localised near the core of a Nielsen-Olesen vortex configuration. We show that an anomaly free theory in 6-dimensions can give rise to an anomalous theory in D=4, which suggests a possibility of consistent regularisation of abelian anomalous chiral gauge theories in four dimensions. We also show that the spectrum of charged bulk fermions has a mass gap.

Black string entropy from anomalous D-brane couplings

The quantum corrections to the counting of statistical entropy for the 5+1-dimensional extremal black string in type-IIB supergravity with two observers are studied using anomalous Wess-Zumino actions for the corresponding intersecting D-brane description. The electric-magnetic duality symmetry of the anomalous theory implies a new symmetry between D-string and D-fivebrane sources and renders opposite sign for the RR charge of one of the intersecting D-branes relative to that of the black string. The electric-magnetic symmetric Hilbert space decomposes into subspaces associated with interior and exterior regions and it is shown that, for an outside observer, the expectation value of a horizon area operator agrees with the deviation of the classical horizon area in going from extremal to near-extremal black strings.

Stochastic Methods and Anomalous Transport

Variety of diagnostics indicate a wide spectrum of fluctuations δn, δẼ, δB, δT which are probably due to micro-instabilities. Anomalous transport theory tries to explain the observed transport in terms of the measured fluctuations. We consider some recent applications of stochastic methods to plasmas in a turbulent state.

THE LAX PAIR OF A GENERALIZED THIRRING MODEL

The system of coupled nonlinear partial differential equations called the Massive Thirring Model is reviewed. In particular it is analyzed in the chiral fermion version, which is extended by introducing a local gauge symmetry in place of the usual global symmetry. This is done by minimally coupling the fermions with a SU L(2) ⊗ SU R(2) gauge potential. Following the formalism of path integrals, we then formulate the study of chiral gauge anomalies in the quantum theory of this gauge extended model. The ultimate goal of it would be to compute the divergence of the chiral fermion current for a nonlinear anomalous theory. Actually, in this work we merely exhibit the Lax pair representation of the system of partial differential equations just derived; it holds to the first order approximation in the infinitesimal gauge parameters and coupling constants present. Our aim is to hint a motivation in searching for explicit solutions of anomalous nonlinear gauge field theories, at least in simple cases.

Black string entropy from anomalous D-brane couplings

The quantum corrections to the counting of statistical entropy for the 5+1-dimensional extremal black string in type-IIB supergravity with two observers are studied using anomalous Wess-Zumino actions for the corresponding intersecting D-brane description. The electric-magnetic duality symmetry of the anomalous theory implies a new symmetry between D-string and D-fivebrane sources and renders opposite sign for the RR charge of one of the intersecting D-branes relative to that of the black string. The electric-magnetic symmetric Hilbert space decomposes into subspaces associated with interior and exterior regions and it is shown that, for an outside observer, the expectation value of a horizon area operator agrees with the deviation of the classical horizon area in going from extremal to near-extremal black strings.

ANOMALOUS CHIRAL ACTION FROM THE PATH INTEGRAL

By generalizing the Fujikawa approach, we show in the path integral formalism: (1) how the infinitesimal variation of the fermion measure can be integrated to obtain the full anomalous chiral action; (2) how the action derived in this way can be identified as the Chern–Simons term in five dimensions, if the anomaly is consistent; (3) how the regularization can be carried out, so as to lead to the consistent anomaly and not to the covariant anomaly. We consider a massless left-handed fermion interacting with a non-Abelian gauge field. The gauge field also interacts with a set of Goldstone bosons, so that a gauge-invariant configuration of the gauge field exists. We use Schwinger's "proper time" representation of the Green's function and the guage-invariant point-splitting technique, and find that the consistency requirement and the point-splitting technique allow both an anomalous and a nonanomalous action. In the end, the nature of the vacuum determines whether we have an anomalous theory or a nonanomalous theory.

Algebraic Isomorphism in Two-Dimensional Anomalous Gauge Theories

The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert space associated with the Wightman functions. The isomorphism between gauge noninvariant and gauge invariant descriptions of the anomalous theory is established in terms of the corresponding field algebras. We show that (i) theΘ-vacuum representation and (ii) the suggested equivalence of vector Schwinger model and chiral Schwinger model cannot be established in terms of the intrinsic field algebra