Anomaly Cancellation Research Articles

Discrete gauge anomalies and instantons

We revisit anomalous phases related to large gauge transformations, such as the Witten anomaly. The latter, known to plague d = 4 Sp(k) theories, is well-understood in terms of π4(Sp(k)) = ℤ2, but it also has an oblique relation to the instantons, labeled by π3(G) = ℤ, via the fermion zero mode counting. We revisit this relation and point out how SU(N) theories escape an anomalous sign of the latter type, only thanks to the perturbative anomaly cancelation condition that restricts the chiral fermion spectrum. This leads to the question of what happens if the latter, more mundane anomaly is canceled by an inflow instead. After raising an open question about fractional D3 probe theories, we explore the simplest bottom-up model of such a kind, due to Witten and Yonekura, from which we find the relevant chiral theories to be free of such a disease despite the unrestricted chiral spectra. We close with a simple but often-overlooked observation about how fermionic zero modes enter physics differently between Euclidean and Lorentzian descriptions and point out a related issue in d = 3.

Two-dimensional gauge anomalies and p-adic numbers

We show how methods of number theory can be used to study anomalies in gauge quantum field theories in spacetime dimension two. To wit, the anomaly cancellation conditions for the abelian part of the local anomaly admit solutions if and only if they admit solutions in the reals and in the p-adics for every prime p and we use this to build an algorithm to find all solutions.

Questions of flavor physics and neutrino mass from a flipped hypercharge

The flavor structure of quarks and leptons is not yet fully understood, but it hints a more fundamental theory of nonuniversal generations. We therefore propose a simple extension of the Standard Model by flipping (i.e., enlarging) the hypercharge U(1)Y to U(1)X⊗U(1)N for which both X and N depend on generations of both quark and lepton. By anomaly cancellation, this extension not only explains the existence of just three fermion generations as observed but also requires the presence of a right-handed neutrino per generation, which motivates seesaw neutrino mass generation. Furthermore, in its minimal version with a scalar doublet and two scalar singlets, the model naturally generates the measured fermion-mixing matrices while it successfully accommodates several flavor anomalies observed in the neutral meson mixings, B-meson decays, lepton-flavor-violating processes of charged leptons, as well as satisfying constraints from particle colliders. Published by the American Physical Society 2024

What Bordism-Theoretic Anomaly Cancellation Can Do for U

We perform a bordism computation to show that the E7(7)(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{7(7)}({\\mathbb {R}})$$\\end{document} U-duality symmetry of 4d N=8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {N}} = 8$$\\end{document} supergravity could have an anomaly invisible to perturbative methods; then we show that this anomaly is trivial. We compute the relevant bordism group using the Adams and Atiyah–Hirzebruch spectral sequences, and we show the anomaly vanishes by computing η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document}-invariants on the Wu manifold, which generates the bordism 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.

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.

An Added Proof of the "Trace Anomaly Redefinition": Equivalent Wick Rotation Conditions

The Chiral Trace Anomaly cancellation in Gravitational Curved Spaces necessitated, due to the presence of the metric inside the action integral, that it is needed for both the “volume” and the “surface” terms, which can both be explicit functions of time, to be resolved and also sufficiently to be brought down by one more dimension. This leads into a description through orbits (close to Euclidean), allowing for a generalization of the Wick rotation and confirming the Trace anomaly redefinition already exposed.

Flipped SU(6) unification of the sequential SU(3)c×SU(3)L×U(1)X model

We propose to partially unify the sequential SU(3)c×SU(3)L×U(1)X model (with β=1/3) into the flipped SU(6) model with the gauge group SU(6)×U(1)K. Gauge anomaly cancellation can easily be satisfied. We discuss the relevant Higgs sector, the low energy model spectrum, and the unification of SU(3)c and SU(3)L gauge couplings. Neutrino mass generation and successful gauge coupling unification can set lower/upper bounds on the breaking scale. The partial proton decay lifetime of various channels, for example, the p→e+π0 channel, in flipped SU(6) GUT are discussed. We find that certain parameter region with M331∼1015 GeV of case II (for case with M331 scale H˜3,8 Higgs field) can predict a partial proton lifetime of order 1034 years for p→e+π0 mode, which can be tested soon by future DUNE and Hyper-Kamiokande experiments. Published by the American Physical Society 2024

Anomaly cancellation in string theory

The anomaly cancellation in superstring theory is known to hold at leading order in the curvature for the gauge groups [Formula: see text] and [Formula: see text]. The coefficients of the next-to-leading order terms may be evaluated, and a mechanism for cancellation is described, which would remain valid at higher genus when there exists a global splitting of the coordinates of supermoduli space. Since the spin-[Formula: see text] fields transform under the adjoint representation in these models, compactification of the heterotic string over [Formula: see text] or a fundamental 12-dimensional theory, from which superstrings are produced through an elliptic fibration, over [Formula: see text], provides another phenomenologically viable theory at lower energies compatible with the standard description of the elementary particle interactions. The 96 spin-[Formula: see text] fields now would transform under the fundamental representation of [Formula: see text] and the spin-one gauge fields would belong to the adjoint representation. The sum of the anomaly polynomials for the particle content of the [Formula: see text] model vanishes at [Formula: see text]. The contributions to the gravitational anomaly from the particles and antiparticles cancel by the CPT theorem and the duality transformations of polynomials of degree 6 in the curvature and the field strength. The existence of the interaction of a spin-2 charge, which is conserved only over a finite time interval, can be traced to nonlocal terms in the reduction of the string field theory to the gravitational sector. The source of the global gravitational anomaly cancellation in the modular form equations derived from an elliptic fibration of a 12-dimensional theory would restrict the compactifications and provide a method for preserving the absence of anomalies in four dimensions.

Dark matter interactions from an extra U(1) gauge symmetry with kinetic mixing and Higgs charge* *Supported by the National Natural Science Foundation of China (12135014)

We investigate fermionic dark matter interactions with standard model particles from an additional gauge symmetry, assuming kinetic mixing between the and gauge fields as well as a nonzero charge of the Higgs doublet. To ensure gauge-invariant Yukawa interactions and the cancellation of gauge anomalies, standard model fermions are assigned Y-sequential charges proportional to the Higgs charge. Although the Higgs charge should be small owing to collider constraints, it is useful to decrease the effective cross section of dark matter scattering off nucleons by two orders of magnitude to easily evade direct detection bounds. After performing numerical scans in the parameter space, we find that the introduction of the Higgs charge can also enhance the dark matter relic density by at least two orders of magnitude. In the case where the resonance effect is important for dark matter freeze-out, when the observed relic density and direct detection constraints are tangled, the Higgs charge can expand physical windows to some extent by relieving the tension between the relic density and direct detection.

Anomaly cancellation in the lattice effective electroweak theory

The anomaly cancellation is at the basis of the perturbative consistence of the Standard Model, and it provides a partial explanation of charge quantization. We consider an effective electroweak theory on a lattice, with a quartic interaction describing the weak forces and an interaction with the e.m. field. We prove the validity of the anomaly cancellation at a non-perturbative level and with a finite lattice cutoff, even if the lattice breaks some important symmetries, on which perturbative arguments for the cancellation are based. The method of the proof has analogies with the one adopted for establishing the universality in transport of quantum materials.

Integer solutions to the anomaly equations for a class of chiral gauge theories

We find all the integer charge solutions to the equations for the cancellation of local gauge anomalies in a class of gauge theories that extend the Standard Model (SM) by a gauge group of the form $G\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$, where $G$ is an arbitrary semisimple compact Lie group. The SM fermions are assumed to be neutral under $G\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge interactions, while the new fermions transform in nontrivial representations of both the new and the SM gauge groups. Our analysis is valid also when the latter is embedded in an arbitrary semisimple compact Lie group. Theories with this structure have recently been studied as models of composite axions based on accidental symmetries and can provide a field theory resolution to the axion quality problem. We apply our results to cases of phenomenological interest and prove the existence of charge assignments with Peccei-Quinn symmetry protected up to dimension 18.

Scale-invariant 3-3-1-1 model with B−L symmetry

Motivated by a possible interplay between the mechanism of dynamical symmetry breaking and the seesaw mechanism for generating fermion masses, we present a scale-invariant model that extends the gauge symmetry of the Standard Model electroweak sector to SU(3)$_L\otimes$U(1)$_X\otimes$U(1)$_N$, with a built-in $B-L$ symmetry. The model is based on the symmetry structure of the known 3-3-1 models and, thus, it relates the number of the three observed fermion generations with the cancellation of gauge anomalies. Symmetry breaking is triggered via the Coleman-Weinberg mechanism taking into account a minimal set of scalar field multiplets. We establish the stability conditions for the tree-level scalar potential imposing the copositivity criteria and use the method of Gildener-Weinberg for computing the one-loop effective potential when one has multiple scalar fields. With the addition of vectorial fermions, getting their mass mainly through the vacuum expectation value of scalar singlets at $10^3$ TeV, the $B-L$ symmetry leads to textures for the fermion mass matrices, allowing seesaw mechanisms for neutrinos and quarks to take place. In particular, these mechanisms could partly explain the mass hierarchies of the quarks. Once the breakdown of the SU(3)$_L$ symmetry is supposed to occur around 10 TeV, the model also predicts new particles with TeV-scale masses, such as a neutral scalar, $H_{1}$, a charged scalar, $H^\pm$, and the gauge bosons $Z^{\prime}$, $W^{\prime\pm}$ and $Y^0$, that could be searched with the high-luminosity LHC.

Proton stability: From the standard model to beyond grand unification

A proton is known for its longevity, but what is its lifetime? While many grand unified Theories predict the proton decay with a finite lifetime, we show that the Standard Model (SM) and some versions of ultraunification (which replace sterile neutrinos with new exotic gapped/gapless sectors, e.g., topological or conformal field theory under global anomaly cancellation constraints) with a discrete baryon plus lepton symmetry permit a stable proton. For the 4D SM with Lie group ${G}_{{\mathrm{SM}}_{q}}\ensuremath{\equiv}\frac{\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{\stackrel{\texttildelow{}}{Y}}}{{\mathbb{Z}}_{q}}$ of $q=1$, 2, 3, 6 and ${N}_{f}$ families of 15 or 16 Weyl fermions, in addition to the continuous baryon minus lepton $\mathrm{U}(1{)}_{\mathbf{B}\ensuremath{-}\mathbf{L}}$ symmetry, there is also a compatible discrete baryon plus lepton ${\mathbb{Z}}_{2{N}_{f},\mathbf{B}+\mathbf{L}}$ symmetry. The ${\mathbb{Z}}_{2{N}_{f},\mathbf{B}+\mathbf{L}}$ is discrete due to the Adler-Bell-Jackiw anomaly under the BPST SU(2) instanton. Although both $\mathrm{U}(1{)}_{\mathbf{B}\ensuremath{-}\mathbf{L}}$ and ${\mathbb{Z}}_{2{N}_{f},\mathbf{B}+\mathbf{L}}$ symmetries are anomaly free under the dynamically gauged ${G}_{{\mathrm{SM}}_{q}}$, it is important to check whether they have mixed anomalies with the gravitational background field (spacetime diffeomorphism under Spin group rotation) and higher symmetries (whose charged objects are Wilson electric or 't Hooft magnetic line operators) of SM. We can also replace the $\mathrm{U}(1{)}_{\mathbf{B}\ensuremath{-}\mathbf{L}}$ with a discrete variant ${\mathbb{Z}}_{4,X}$ for $X\ensuremath{\equiv}5(\mathbf{B}\ensuremath{-}\mathbf{L})\ensuremath{-}\frac{2}{3}\stackrel{\texttildelow{}}{Y}$ of electroweak hypercharge $\stackrel{\texttildelow{}}{Y}$. We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4D SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM's deformation class. We discuss the proton stability of the SM and ultraunification in the presence of discrete $\mathbf{B}+\mathbf{L}$ symmetry protection, in particular $(\mathrm{U}(1{)}_{\mathbf{B}\ensuremath{-}\mathbf{L}}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2{N}_{f},\mathbf{B}+\mathbf{L}})/{\mathbb{Z}}_{2}^{F}$ or $({\mathbb{Z}}_{4,X}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2{N}_{f},\mathbf{B}+\mathbf{L}})/{\mathbb{Z}}_{2}^{F}$ with the fermion parity ${\mathbb{Z}}_{2}^{F}$.

Symmetric Mass Generation

The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group, also applicable to chiral fermions with anomaly-free chiral symmetries. This new mechanism is generally referred to as the symmetric mass generation (SMG). It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes the current numerical results, introduces an unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and presents an overview of various features and applications of SMG.

Seesaw mechanism in the R-parity-violating supersymmetric standard model with the gauged flavor U(1)X symmetry

Abstract We study the seesaw mechanism in the supersymmetric standard model (SSM) with the ${\mathbb {Z}}_3$ symmetry called matter triality (M3). The Abelian discrete symmetry prohibits the baryon number violation operators at the (non-)renormalizable level, which ensures proton longevity. The cubic coupling by right-handed neutrinos generates the Majorana mass term after the right-handed sneutrinos develop into the vacuum expectation values. Due to the R-parity violation, the active neutrino masses can be generated not only from the mixings with the right-handed neutrinos but also from those with the minimal SSM neutralinos. We propose a model where M3 is embedded in the gauged flavor symmetry. The flavor charges are constrained by the anomaly cancellation conditions and the requirements to realize the fermion masses and mixing angles in the quark and lepton sectors. We analyze the assignments of the flavor charge, and show that the sterile neutrino mass is allowed to be below the soft supersymmetry-breaking scale, which is constrained by the half-lifetime of the neutrinoless double beta decay.

Effective Dirac Neutrino Mass Operator in the Standard Model With a Local Abelian Extension

We present 48 types of solutions to the anomaly cancellation conditions of local Abelian extensions of the Standard Model (SM) with right-handed SM-singlet chiral fermions. At least two of them acquire effective light Dirac neutrino masses, while the others get heavy masses from the spontaneous symmetry breaking of the local Abelian symmetry, forming a dark sector with multi-component and multi-generational fermionic dark matter. The corresponding effective Dirac neutrino mass operator can be realized at tree-level or radiatively by introducing extra scalars, and in some cases after imposing extra scotogenic conditions. The Dirac Zee model with Dirac fermionic dark matter is presented as an example of model where the neutrino and dark matter phenomenology are basically independent of each other.

Twistorial cohomotopy implies Green–Schwarz anomaly cancellation

We characterize the integral cohomology and the rational homotopy type of the maximal Borel-equivariantization of the combined Hopf/twistor fibration, and find that subtle relations satisfied by the cohomology generators are just those that govern Hořava–Witten’s proposal for the extension of the Green–Schwarz mechanism from heterotic string theory to heterotic M-theory. We discuss how this squares with the Hypothesis H that the elusive mathematical foundation of M-theory is based on charge quantization in tangentially twisted unstable Cohomotopy theory.

Model characterization and dark matter in the secluded U(1)′ model

We consider a class of $U(1)^\prime$-extended MSSM in which the $U(1)^{\prime}$ symmetry is broken by vacuum expectation values (VEVs) of four MSSM singlet fields. While one MSSM singlet field interacts with the MSSM Higgs fields, three of them interact only with each other in forming a secluded sector. Assigning universal $U(1)^{\prime}$ charges for three families, the anomaly cancellation condition requires exotic fields which are assumed to be heavy and decoupled. We discuss a variety of $U(1)^{\prime}$ charge assignments and anomaly cancellation, $Z^{\prime}/Z$ hierarchy, neutralinos, charginos and the Higgs sector. We find that the typical spectra involve two CP-odd Higgs bosons lighter than about 200 GeV and 600 GeV respectively, which are mostly formed by the MSSM singlet fields. If the relic density of dark matter is saturated only by a neutralino, compatible solutions predict LSP neutralinos formed by the MSSM singlet fields in the mass scales below about 600 GeV, while it is possible to realize MSSM neutralino LSP above these mass scales. One can classify the implications in three scenarios. Scenario I involves NLSP charginos, while Scenario II involves charginos which do not participate coannihilation processes with the LSP neutralino. These two scenarios predict MSSM singlet LSP neutralinos, while Scenario I leads to larger scattering cross-sections of dark matter. Scenario III has the solutions in which the MSSM neutralinos are considerably involved in LSP decomposition which yields very large scattering cross-section excluded by the direct detection experiments.

Solving gauge anomaly equations in the standard model using the method of chords

In a recent paper, Allanach et al (2020 J. High Energy Phys. JHEP05(2020)065) introduced a geometric method to solve the anomaly cancellation equations for a U(1) gauge theory with an arbitrary number of charges—the method of chords known in Diophantine analysis. We extend their result to non-abelian gauge groups, and show that this method can be used to find the general solution to the anomaly cancellation equations for a theory with the standard model gauge group on a curved background. Given K charges in (2, 3), L charges in (2, 1), M charges in (1, 3), and N charges in (1, 1) representations of SU(2) × SU(3), the equations reduce to a homogeneous cubic Diophantine equation in K + L + M + N − 4 variables.