Gauge Anomalies Research Articles

Wess-Zumino-Witten terms of Sp QCD by bordism theory

We investigate the four-dimensional Wess-Zumino-Witten (WZW) terms within the framework of Sp quantum chromodynamics (QCD) using invertible field theory through bordism theory. We present a novel approach aimed at circumventing both perturbative and non-perturbative gauge anomalies on spacetime manifolds endowed with spin structures. We study both ungauged and gauged WZW terms including the problems of the topological consistency of gauged WZW terms.

Lepton and baryon numbers as local gauge symmetries

A simple theory where the total lepton number is a local gauge symmetry is proposed. In this context, the gauge anomalies are canceled with the minimal number of extra fermionic fields and one predicts that the neutrinos are Majorana fermions. The properties of the neutrino sector are discussed, showing that this theory predicts a 3+2 light neutrino sector. We show that using the same fermionic fields one can gauge the baryon number and define a simple theory where the lepton and baryon numbers can be spontaneously broken at the low scale in agreement with experiments. Published by the American Physical Society 2024

Constraining νSMEFT coefficients: The case of the extra U(1)′

We study the constraints on low-energy coefficients of the νSMEFT generalization of the Standard Model effective theory in the simple case of a U(1)′ enlargement of the Standard Model gauge group. In particular, we analyze the constraints imposed by the requirement that the extended theory remains free of gauge anomalies. We present the cases of explicit realizations, showing the obtained correlations among the coefficients of d=6 operators. Published by the American Physical Society 2024

Deconstructing flavor anomalously

Flavor deconstruction refers to ultraviolet completions of the Standard Model where the gauge group is split into multiple factors under which fermions transform non-universally. We propose a mechanism for charging same-family fermions into different factors of a deconstructed gauge theory in a way that gauge anomalies are avoided. The mechanism relies in the inclusion of a strongly-coupled sector, responsible of both anomaly cancellation and the breaking of the non-universal gauge symmetry. As an application, we propose different flavor deconstructions of the Standard Model that, instead of complete families, uniquely identify specific third-family fermions. All these deconstructions allow for a new physics scale that can be as low as few TeV and provide an excellent starting point for the explanation of the Standard Model flavor hierarchies.

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.

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 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.

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.

Asymptotic ultraviolet-safe unification of gauge and Yukawa couplings: The exceptional case

The ultimate dream of unification models consists in combining both gauge and Yukawa couplings into one unified coupling. This is achieved by using a supersymmetric exceptional E6 gauge symmetry together with asymptotic unification in compact five-dimensional space-time. The ultraviolet fixed point requires exactly three fermion generations: one in the bulk, and the two light ones localised on the SO(10) boundary in order to cancel gauge anomalies. A second option allows to preserve baryon number and to lower the compactification scale down to the typical scales of the intermediate Pati-Salam gauge theory.

Chiral Gauge Theory at the Boundary between Topological Phases.

I demonstrate how chiral fermions with an exact gauge symmetry can appear on the d-dimensional boundary of a finite volume (d+1)-dimensional manifold, without any light mirror partners. The condition for the d-dimensional boundary theory to be local is that gauge anomalies cancel and that the volume be large. This can likely be achieved on a lattice and provides a new paradigm for the lattice regularization of chiral gauge theories.

Anomalies of generalized symmetries from solitonic defects

We propose the general idea that ’t Hooft anomalies of generalized global symmetries can be understood in terms of the properties of solitonic defects, which generically are non-topological defects. The defining property of such defects is that they act as sources for background fields of generalized symmetries. ’t Hooft anomalies arise when solitonic defects are charged under these generalized symmetries. We illustrate this idea for several kinds of anomalies in various spacetime dimensions. A systematic exploration is performed in 3d for 0-form, 1-form, and 2-group symmetries, whose ’t Hooft anomalies are related to two special types of solitonic defects, namely vortex line defects and monopole operators. This analysis is supplemented with detailed computations of such anomalies in a large class of 3d gauge theories. Central to this computation is the determination of the gauge and 0-form charges of a variety of monopole operators: these involve standard gauge monopole operators, but also fractional gauge monopole operators, as well as monopole operators for 0-form symmetries. The charges of these monopole operators mainly receive contributions from Chern-Simons terms and fermions in the matter content. Along the way, we interpret the vanishing of the global gauge and ABJ anomalies, which are anomalies not captured by local anomaly polynomials, as the requirement that gauge monopole operators and mixed monopole operators for 0-form and gauge symmetries have non-fractional integer charges.

Z′ induced forward dominant processes in μTRISTAN experiment

General U(1) extension of the Standard Model (SM) is a well motivated beyond the Standard Model (BSM) scenario where three generations of right handed neutrinos (RHNs) are introduced to cancel gauge and mixed gauge-gravity anomalies. After the U(1)X is broken, RHNs participate in the seesaw mechanism to generate light neutrino masses satisfying neutrino oscillation data. In addition to that, a neutral gauge boson Z′ is evolved which interacts with the left and right handed fermions differently manifesting chiral nature of the model which could be probed in future collider experiments. As a result, if we consider μ+e− and μ+μ+ collisions in μTRISTAN experiment Z′ mediated 2→2 scattering will appear in t− and u-channels depending on the initial and final states being accompanied by the photon and Z mediated interactions. This will result well motivated resulting forward dominant scenarios giving rise to sizable left-right asymmetry. Estimating constraints on general U(1) coupling from LEP-II and LHC for different U(1)X charges, we calculate differential and integrated scattering cross section and left-right asymmetry for μ+e−→μ+e− and μ+μ+→μ+μ+ processes which could be probed at μTRISTAN experiment further enlightening the interaction between Z′ and charged leptons and the U(1)X breaking scale.

WZW in the lightlike directions

Dimensional reduction of the M5 brane on a Lorentzian manifold along a lightlike direction results in a five-dimensional gauge theory, which can be reformulated covariantly in six dimensions, where one puts the Lie derivatives along the lightlike direction of all fields to zero up to a gauge equivalence as constraints. We find gauge and supersymmetry anomalies for certain Lorentzian six-manifolds. We cancel these anomalies by adding a certain WZW theory in the 2d space that is spanned by two lightlike directions.

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

Dijet and electroweak limits on a Z′ boson coupled to quarks

An insightful way of presenting the LHC limits on dijet resonances is the coupling-mass plot for a Z′ boson that has flavor-independent quark interactions. This also illustrates the comparison of low-mass LHC sensitivity with constraints on the flavor-independent Z′ boson from electroweak and quarkonium measurements. To derive these constraints, we compute the Z′ mixing with the Z, the photon, and the ϒ meson, emphasizing the logarithmic dependence on the masses of the new electroweak-charged fermions (“anomalons”) required to cancel the gauge anomalies. We update the coupling-mass plot, extending it for Z′ masses from 5 GeV to 5 TeV. Published by the American Physical Society 2024

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.

A heterotic Kodaira-Spencer theory at one-loop

We consider a heterotic version of six-dimensional Kodaira-Spencer gravity derived from the heterotic superpotential. We compute the one-loop partition function and find it can be expressed as a product of holomorphic Ray-Singer torsions. We discuss its topological properties and potential gauge and gravitational anomalies. We show these anomalies can be cancelled using Green-Schwarz-like counter-terms. We also discuss the dependence on the background geometry, and in particular the choice of hermitian metric needed for quantisation. Given suitable topological constraints, this dependence may again be cancelled by the addition of purely background-dependent counter-terms. We also explain how our methods provide the one-loop partition functions of a large class of more general holomorphic field theories in terms of holomorphic Ray-Singer torsions.

Axion effective potentials induced by heavy sterile fermions

A model of (3 + 1)-dimensional leptogenesis, proposed previously by the authors, requires a CPT Violating (CPTV) background of the Kalb–Ramond (KR) axion field. The KR axion is a pseudoscalar, which is dual to the field strength of the spin-one field present in the massless gravitational multiplet in the theory of closed bosonic strings (compactified to four dimensions). Microscopic models for the emergence of such backgrounds are provided both by low-energy string-inspired gravitational theories with torsion (including (primordial) gravitational and axial gauge anomalies) and by Einstein–Cartan gravity, a closely related simpler model. In this work we examine the pseudoscalar quanta of the KR axion in this background using the methods of effective field theory. In our model for leptogenesis there is a single sterile right-handed neutrino (RHN) with mass m_N. At energies lower than m_N, an axion potential is derived by integrating out at one loop the sterile neutrino in the spirit of effective field theory. The stability of this axion potential is important for the viability of our model. The vacuum of this potential is generally metastable. The stability of the vacuum is determined by the ratio of the torsion-induced-axion coupling (which depends on the string mass scale) to m_N, which should be larger or equal to one, for the validity of our effective field theory. The vacuum is metastable only for axion couplings much larger than the sterile neutrino mass (large string mass scales, e.g. comparable to the four-dimensional Planck mass), with a lifetime much larger than the age of the observable Universe. By contrast, if axion couplings are comparable to the RHN mass the false vacuum is highly unstable, with a lifetime much smaller than the age of the observable Universe; in this case the CPTV leptogenesis scenario is not viable.

Background Independence and the Adler–Bardeen Theorem

We prove that for renormalizable Yang–Mills gauge theory with arbitrary compact gauge group (of at most a single abelian factor) and matter coupling, the absence of gauge anomalies can be established at the one-loop level. This proceeds by relating the gauge anomaly to perturbative agreement, which formalizes background independence.

On anomalies and gauging of U(1) non-invertible symmetries in 4d QED

In this work we propose a way to promote the anomalous axial U(1)U(1) transformations to exact non-invertible U(1)U(1) symmetries. We discuss the procedure of coupling the non-invertible symmetry to a (dynamical or background) gauge field. We show that as part of the gauging procedure, certain constraints are imposed to make the gauging consistent. The constraints emerge naturally from the form of the non-invertible U(1)U(1) conserved current. In the case of dynamical gauging, this results in new type of gauge theories we call non-invertible gauge theories: These are gauge theories with additional constraints that cancel the would-be gauge anomalies. By coupling to background gauge fields, we can discuss ’t-Hooft anomalies of non-invertible symmetries. We show in an example that the matching conditions hold but they are realized in an unconventional way. Turning on non-trivial background for the non-invertible gauge field changes the vacuum even when the symmetry is not broken and the background is very weak. The anomalies are then matched by the appearance of solitons in the new vacuum.