Anomaly-free Condition Research Articles

Classification of interacting Dirac semimetals

Topological band theory predicts a Z classification of three-dimensional (3D) Dirac semimetals (DSMs) at the single-particle level. Namely, an arbitrary number of identical bulk Dirac nodes will always remain locally stable and gapless in the single-particle band spectrum, as long as the protecting symmetry is preserved. In this work we find that this single-particle classification for Cn-symmetric DSMs will break down to Zn/gcd(2,n) in the presence of symmetry-preserving electron interactions. Our theory is based on a dimensional reduction strategy which reduces a 3D Dirac fermions to one-dimensional building blocks, i.e., vortex-line modes, while respecting all the key symmetries. Using bosonization technique, we find that there exists a minimal number N=n/gcd(2,n) such that the collection of vortex-line modes in N copies of DSMs can be symmetrically eliminated via four-fermion interactions. While this gapping mechanism does not have any free-fermion counterpart, it yields an intuitive “electron-trion coupling” picture. By developing a topological field theory for DSMs and further checking the anomaly-free condition, we independently arrive at the same classification results. Our theory paves the way for understanding topological crystalline semimetallic phases in the strongly correlated regime. Published by the American Physical Society 2024

Fusion rules and shrinking rules of topological orders in five dimensions

As a series of work about 5D (spacetime) topological orders, here we employ the path-integral formalism of 5D topological quantum field theory (TQFT) established in Zhang and Ye, JHEP04 (2022) 138 to explore non-Abelian fusion rules, hierarchical shrinking rules and quantum dimensions of particle-like, loop-like and membrane-like topological excitations in 5D topological orders. To illustrate, we focus on a prototypical example of twisted BF theories that comprise the twisted topological terms of the BBA type. First, we classify topological excitations by establishing equivalence classes among all gauge-invariant Wilson operators. Then, we compute fusion rules from the path-integral and find that fusion rules may be non-Abelian; that is, the fusion outcome can be a direct sum of distinct excitations. We further compute shrinking rules. Especially, we discover exotic hierarchical structures hidden in shrinking processes of 5D or higher: a membrane is shrunk into particles and loops, and the loops are subsequently shrunk into a direct sum of particles. We obtain the algebraic structure of shrinking coefficients and fusion coefficients. We compute the quantum dimensions of all excitations and find that sphere-like membranes and torus-like membranes differ not only by their shapes but also by their quantum dimensions. We further study the algebraic structure that determines anomaly-free conditions on fusion coefficients and shrinking coefficients. Besides BBA, we explore general properties of all twisted terms in 5D. Together with braiding statistics reported before, the theoretical progress here paves the way toward characterizing and classifying topological orders in higher dimensions where topological excitations consist of both particles and spatially extended objects.

The heterotic 𝐺₂ system on contact Calabi–Yau 7-manifolds

We obtain non-trivial approximate solutions to the heterotic G 2 \mathrm {G}_2 system on the total spaces of non-trivial circle bundles over Calabi–Yau 3 3 -orbifolds, which satisfy the equations up to an arbitrarily small error, by adjusting the size of the S 1 S^1 fibres in proportion to a power of the string constant α ′ \alpha ’ . Each approximate solution provides a cocalibrated G 2 \mathrm {G}_2 -structure, the torsion of which realises a non-trivial scalar field, a constant (trivial) dilaton field and an H H -flux with non-trivial Chern–Simons defect. The approximate solutions also include a connection on the tangent bundle which, together with a non-flat G 2 \mathrm {G}_2 -instanton induced from the horizontal Calabi–Yau metric, satisfy the anomaly-free condition, also known as the heterotic Bianchi identity. The approximate solutions fail to be genuine solutions solely because the connections on the tangent bundle are only G 2 \mathrm {G}_2 -instantons up to higher order corrections in α ′ \alpha ’ .

Lieb–Schultz–Mattis theorem and the filling constraint

Following recent developments in the classification of bosonic short-range entangled phases, we examine many-body quantum systems whose ground state fractionalization obeys the Lieb-Schultz-Mattis (LSM) theorem. We generalize the topological classification of such phases by LSM anomalies (arXiv:1907.08204) to take magnetic and non-symmorphic lattice effects into account, and provide direct computations of the LSM anomaly in specific examples. We show that the anomaly-free condition coincides with established filling constraints (arXiv:1705.09298, arXiv:1505.04193), and we also derived new ones on novel crystalline quantum systems.

A Family-nonuniversal [formula omitted] Model for Excited Beryllium Decays

Excited beryllium has been observed to decay into electron-positron pairs with a 6.8σ anomaly. The process is properly explained by a 17 MeV proto-phobic vector boson. In present work, we consider a family-nonuniversal U(1)′ that is populated by a U(1)′ gauge boson Z′ and a scalar field S, charged under U(1)′ and singlet under the Standard Model (SM) gauge symmetry. The SM chiral fermion and scalar fields are charged under U(1)′ and we provide them to satisfy the anomaly-free conditions. The Cabibbo-Kobayashi-Maskawa (CKM) matrix is reproduced correctly by higher-dimension Yukawa interactions facilitated by S. The vector and axial-vector current couplings of the Z′ boson to the first generation of fermions do satisfy all the bounds from the various experimental data. The Z′ boson can have kinetic mixing with the hypercharge gauge boson and S can directly couple to the SM-like Higgs field. The kinetic mixing of Z′ with the hypercharge gauge boson, as we show by a detailed analysis, generates the observed beryllium anomaly. We find that beryllium anomaly can be properly explained by a MeV-scale sector with a minimal new field content. The minimal model we construct forms a framework in which various anomalous SM decays can be discussed.

Inflation and leptogenesis in a U(1) -enhanced supersymmetric model

Motivated by the flavored Peccei-Quinn symmetry for unifying flavor physics and string theory, we investigate a supersymmetric extension of standard model (SM) for an explanation of inflation and leptogenesis by introducing $U(1)$ symmetries such that the $U(1)$-$[gravity]^2$ anomaly-free condition together with the SM flavor structure demands additional sterile neutrinos as well as no axionic domain-wall problem. Such additional neutrinos may play a crucial role as a bridge between leptogenesis and new neutrino oscillations along with high energy cosmic events. In a realistic moduli stabilization, we show that the moduli backreaction effect on the inflationary potential leads to the energy scale of inflation with the inflaton mass in a way that the power spectrum of the curvature perturbation and the scalar spectral index are to be well fitted with the latest Planck observation. We suggest that a new leptogenesis scenario could naturally be implemented via Affleck-Dine mechanism. So we show that the resultant baryon asymmetry, constrained by the sum of active neutrino masses and new high energy neutrino oscillations, crucially depends on the reheating temperature $T_{\rm reh}$. And we show that the model has a preference on $T_{\rm reh}\sim10^3$ TeV, which is compatible with the required $T_{\rm reh}$ to explain the baryon asymmetry of the Universe.

Fermion masses and flavor mixings and strong CP problem

For all the success of the Standard Model (SM), it is on the verge of being surpassed. In this regard we argue, by showing a minimal flavor-structured model based on the non-Abelian discrete SL2(F3) symmetry, that U(1) mixed-gravitational anomaly cancellation could be of central importance in constraining the fermion contents of a new chiral gauge theory. Such anomaly-free condition together with the SM flavor structure demands a condition k1X1/2=k2X2 with Xi being a charge of U(1)Xi and ki being an integer, both of which are flavor dependent. We show that axionic domain-wall condition NDW with the anomaly free-condition depends on both U(1)X charged quark and lepton flavors; the seesaw scale congruent to the scale of Peccei–Quinn symmetry breakdown can be constrained through constraints coming from astrophysics and particle physics. Then the model extended by SL2(F3)×U(1)X symmetry can well be flavor-structured in a unique way that NDW=1 with the U(1)X mixed-gravitational anomaly-free condition demands additional Majorana fermion and the flavor puzzles of SM are well delineated by new expansion parameters expressed in terms of U(1)X charges and U(1)X-[SU(3)C]2 anomaly coefficients. And the model provides remarkable results on neutrino (hierarchical mass spectra and unmeasurable neutrinoless-double-beta decay rate together with the predictions on atmospheric mixing angle and leptonic Dirac CP phase favored by the recent long-baseline neutrino experiments), QCD axion, and flavored-axion.

Axion and neutrino physics in aU(1)-enhanced supersymmetric model

Motivated by the flavored Peccei-Quinn symmetry for unifying the flavor physics and string theory, we construct an explicit model by introducing a $U(1)$ symmetry such that the $U(1)_X$-$[gravity]^2$ anomaly-free condition together with the standard model flavor structure demands additional sterile neutrinos as well as no axionic domain-wall problem. Such additional sterile neutrinos play the role of a realization of baryogenesis via a new Affleck-Dine leptogenesis. We provide grounds for that the $U(1)_X$ symmetry could be interpreted as a fundamental symmetry of nature. The model will resolve rather recent, but fast-growing issues in astro-particle physics, including leptonic mixings and CP violation in neutrino oscillation, high-energy neutrinos, QCD axion, and axion cooling of stars. The QCD axion decay constant, through its connection to the astrophysical constraints of stellar evolution and the SM fermion masses, is shown to be fixed at $F_A=1.30^{+0.66}_{-0.54}\times10^{9}$ GeV (consequently, its mass is $m_a=4.34^{+3.37}_{-1.49}$ meV and axion-photon coupling is $|g_{a\gamma\gamma}|=1.30^{+1.01}_{-0.45}\times10^{-12}\,{\rm GeV}^{-1}$). Interestingly enough, we show that neutrino oscillations at low energies could be connected to astronomical-scale baseline neutrino oscillations. The model predicts non-observational neutrinoless double beta ($0\nu\beta\beta$) decay rate as well as a remarkable pattern between leptonic Dirac CP phase ($\delta_{CP}$) and atmospheric mixing angle ($\theta_{23}$); {\it e.g.} $\delta_{CP}\simeq220^{\circ}-240^{\circ}$, $120^{\circ}-140^{\circ}$ for $\theta_{23}=42.3^{\circ}$ for normal mass ordering, and $\delta_{CP}\simeq283^{\circ},250^{\circ},100^{\circ},70^{\circ}$ for $\theta_{23}=49.5^{\circ}$ for inverted one.

Six-dimensional regularization of chiral gauge theories

We propose a regularization of four dimensional chiral gauge theories using six-dimensional Dirac fermions. In our formulation, we consider two different mass terms having domain-wall profiles in the fifth and the sixth directions, respectively. A Weyl fermion appears as a localized mode at the junction of two different domain-walls. One domain-wall naturally exhibits the Stora-Zumino chain of the anomaly descent equations, starting from the axial U(1) anomaly in six-dimensions to the gauge anomaly in four-dimensions. Another domain-wall implies a similar inflow of the global anomalies. The anomaly free condition is equivalent to requiring that the axial U(1) anomaly and the parity anomaly are canceled among the six-dimensional Dirac fermions. Since our formulation is based on a massive vector-like fermion determinant, a non-perturbative regularization will be possible on a lattice. Putting the gauge field at the four-dimensional junction and extending it to the bulk using the Yang-Mills gradient flow, as recently proposed by Grabowska and Kaplan, we define the four-dimensional path integral of the target chiral gauge theory.

Diphoton excess at 750 GeV in leptophobic U(1)′ model inspired by E 6 GUT

We discuss the 750 GeV diphoton excess at the LHC@13TeV in the framework of leptophobic U(1)$^\prime$ model inspired by $E_6$ grand unified theory (GUT). In this model, the Standard Model (SM) chiral fermions carry charges under extra U(1)$^\prime$ gauge symmetry which is spontaneously broken by a U(1)$^\prime$-charged singlet scalar ($\Phi$). In addition, extra quarks and leptons are introduced to achieve the anomaly-free conditions, which is a natural consequence of the assumed $E_6$ GUT. These new fermions are vectorlike under the SM gauge group but chiral under new U(1)$^\prime$, and their masses come entirely from the nonzero vacuum expectation value of $\Phi$ through the Yukawa interactions. Then, the CP-even scalar $h_\Phi$ from $\Phi$ can be produced at the LHC by the gluon fusion and decay to the diphoton via the one-loop diagram involving the extra quarks and leptons, and can be identified as the origin of diphoton excess at 750 GeV. In this model, $h_\Phi$ can decay into a pair of dark matter particles as well as a pair of scalar bosons, thereby a few tens of the decay width may be possible.

Neutrino mass and dark matter from gaugedU(1)B−Lbreaking

We propose a new model where the Dirac mass term for neutrinos, the Majorana mass term for right-handed neutrinos, and the other new fermion masses arise via the spontaneous breakdown of the $\mathrm{U}(1{)}_{\mathrm{B}\ensuremath{-}\mathrm{L}}$ gauge symmetry. The anomaly-free condition gives four sets of assignment of the $\mathrm{B}\ensuremath{-}\mathrm{L}$ charge to new particles, and three of these sets have an associated global $\mathrm{U}(1{)}_{\mathrm{DM}}$ symmetry which stabilizes dark matter candidates. The dark matter candidates contribute to generating the Dirac mass term for neutrinos at the one-loop level. Consequently, tiny neutrino masses are generated at the two-loop level via a type-I-seesaw-like mechanism. We show that this model can satisfy current bounds from neutrino oscillation data, the lepton flavor violation, the relic abundance of the dark matter, and the direct search for the dark matter. This model would be tested at future collider experiments and dark matter experiments.

Application of higher order holonomy corrections to the perturbation theory of cosmology

Applying the higher order holonomy corrections to the perturbation theory of cosmology, the lattice power law of loop quantum cosmology, , is analyzed and the range of β is decided to be [−1,0] which is different from the conventional range −0.1319 > β ⩾ −5/2 (Bojowald M and Hossain G M 2008 Phys. Rev. D 77 023508). At the same time, we find that there is an anomaly-free condition in this theory, and we obtain this condition in the vector and tensor mode. We also find that the nonzero mass of a gravitational wave essentially results from the quantum nature of the Riemannian geometry of loop quantum gravity.

Lattice chirality and the decoupling of mirror fermions

We show, using exact lattice chirality, that partition functions of lattice gauge theories with vectorlike fermion representations can be split into ``light and ``mirror parts, such that the ``light and ``mirror representations are chiral. The splitting of the full partition function into ``light and ``mirror is well defined only if the two sectors are separately anomaly free. We show that only then is the generating functional, and hence the spectrum, of the mirror theory a smooth function of the gauge field background. This explains how ideas to use additional non-gauge, high-scale mirror-sector dynamics to decouple the mirror fermions without breaking the gauge symmetry?for example, in symmetric phases at strong mirror Yukawa coupling?are forced to respect the anomaly-free condition when combined with the exact lattice chiral symmetry. Our results are also useful in explaining a paradox posed by a recent numerical study of the mirror-fermion spectrum in a toy would-be-anomalous two-dimensional theory. In passing, we prove some general properties of the partition functions of arbitrary chiral theories on the lattice that should be of interest for further studies in this field.

Anomalies and graded coisotropic branes

We compute the anomaly of the axial U(1) current in the A-model on a Calabi-Yau manifold, in the presence of coisotropic branes discovered by Kapustin and Orlov. Our results relate the anomaly-free condition to a recently proposed definition of graded coisotropic branes in Calabi-Yau manifolds. More specifically, we find that a coisotropic brane is anomaly-free if and only if it is gradable. We also comment on a different grading for coisotropic submanifolds introduced recently by Oh.

Five-dimensional supergravity dual of a-maximization

We study the five-dimensional supergravity dual of the a-maximization under AdS 5/CFT 4 duality. We firstly show that the a-maximization is mapped to the attractor equation in five-dimensional gauged supergravity, and that the trial a-function is the inverse cube of the superpotential of the five-dimensional theory. There is also a version of a-maximization in which one extremizes over Lagrange multipliers enforcing the anomaly-free condition of the R-symmetry. We identify the supergravity dual of this procedure, and show how the Lagrange multipliers appearing in the supergravity description naturally correspond to the gauge coupling of the superconformal field theory.

Vector Anomaly and Practicality of Light-Front Dynamics

Light-front dynamics (LFD) is like sweeping dirt to a corner to make the rest of the space clean. This feature allows many practical applications of LFD to the phenomenology of particle physics. To strengthen the practicality of LFD, however, it is necessary to check where the dirt is piled and to find ways to handle the associate complications. In this presentation, we discuss an explicit example of a non-vanishing zero-mode contribution to physical amplitudes which has been regarded as one of the typical complications in LFD. In particular, we analyze the vector anomaly occurring in the calculation of the CP-even form factors of the elementary W± gauge bosons and find that the zero-mode contribution to the helicity zero-to-zero amplitude for the W± gauge bosons is crucial for the correct LFD calculations. Further, we confirm that the anomaly-free condition found in the analysis of the axial anomaly can also get rid of the vector anomaly in LFD as well as in the manifestly covariant calculations. Our findings in this work may provide a bottom-up fitness test not only to the LFD calculations but also to the theory itself, whether it is the standard model or any extension of the standard model.

Manifestations of the vector anomaly in covariant and light-front calculations of the anomalous magnetic moment ofW±bosons

In the calculation of the anomalous magnetic moment of ${W}^{\ifmmode\pm\else\textpm\fi{}}$ bosons, we discuss vector anomalies occurring in the fermion loop that spoil the predictive power of the theory. While the previous analyses were limited to using essentially the manifestly covariant dimensional regulation method, we extend the analysis using both the manifestly covariant formulation and the light-front Hamiltonian formulation with several different regularization methods. We find that the zero-mode contribution to the helicity zero-to-zero amplitude for the ${W}^{\ifmmode\pm\else\textpm\fi{}}$ gauge bosons is crucial for the correct light-front (LF) calculations. Further, we confirm that the anomaly-free condition found in the analysis of the axial anomaly can also get rid of the vector anomaly in light-front dynamics (LFD) as well as in the manifestly covariant calculations. Our findings in this work may provide a bottom-up fitness test not only to the LF calculations but also to the theory itself, whether it is any extension of the Standard Model or an effective field theoretic model for composite systems.

A Schematic Model of Leptons and Quarks Based on Majorana Partners

The possible extension of generation structure is investigated on the basis of a composite model, in which leptons and quarks are composed of rishons $T$ with charge 1/3 and purely neutral $V$. In this sub-system, we regard $V$ as the origin of Majorana particles. The seesaw mechanism implies the possible existence of heavy $V$, denoted as $V_B$ in addition to ordinary $V$, denoted as $V_s$. If we regard $V_B$ as a constitute block of leptons and quarks, a new generation scheme arises. This new scheme satisfies the anomaly-free condition.

Non-Anomalous Flavor Symmetries and SU(6) xSU(2)R Model

We introduce the flavor symmetry ZM ×ZN ×D4 into the SU(6) ×SU(2)R string-inspired model. The cyclic group ZM and the dihedral group D4 are R symmetries, while ZN is a non-R symmetry. By imposing the anomaly-free conditions on the model, we obtain a viable solution under many phenomenological constraints coming from the particle spectra. for the neutrino sector, we find a LMA-MSW solution but no SMA-MSW solution. The solution includes phenomenologically acceptable results concerning fermion masses and mixings and also concerning hierarchical energy scales including the GUT scale, the μ scale and the Majorana mass scale of R-handed neutrinos.

Manifestly gauge covariant treatment of lattice chiral fermions. II

We propose a formulation of chiral fermions on a lattice, on the basis of a lattice extension of the covariant regularization scheme in continuum field theory. The species doublers do not emerge. The real part of the effective action is just one-half of that of Dirac-Wilson fermion and is always gauge invariant even with a finite lattice spacing. The gauge invariance of the imaginary part, on the other hand, sets a severe constraint that is a lattice analog of the gauge anomaly-free condition. For real gauge representations, the imaginary part identically vanishes and the gauge invariance becomes exact.