We present a calculable toy model of an axion coupled to magnetic monopoles and electric charges, with manifest electric-magnetic duality. Our axion-photon coupling incurs periodic corrections due to monopoles (equivalently UV instantons), which are large for light monopoles. Axion periodicity is manifestly duality invariant since the axion itself transforms under duality. Our model is the original Seiberg-Witten theory, which naturally hosts an R-axion and light monopoles. We calculate the axionphoton amplitude in different duality frames and prove its duality invariance.

We show that the tree-level amplitude for producing a monopole–antimonopole pair from an electrically charged pair cannot be constructed from the minimal one-photon couplings. Gluing the electric and magnetic three-point vertices gives a nonzero photon-pole contribution, but the resulting magnetic final state has the opposite discrete-symmetry eigenvalue from the electric initial state. Local four-point interactions cannot change the pole contribution fixed by the three-point couplings, so they cannot repair this mismatch. For fermions, the obstruction is specific to the minimal three-point coupling: an independent Pauli form factor supplies a spin-singlet three-point amplitude and allows the symmetry selection rule to be satisfied.

Recently a manifestly gauge invariant formalism for calculating amplitudes in quantum electrodynamics was outlined in which the field strength, rather than the gauge potential, is used as the propagating field. To demonstrate the utility of this formalism we calculate the axial and gauge anomalies explicitly in theories with both electrically and magnetically charged particles. Usually the gauge anomaly is identified as an amplitude that (in certain theories) fails to be gauge invariant, so it seems particularly enlightening to understand it in a manifestly gauge invariant formalism. We find that the three photon amplitude is still anomalous in these same theories because it depends explicitly upon the choice of the Stokes surface needed to couple the field strength to sources, so the gauge anomaly arises from geometric considerations.

We study the implications of noninvertible chiral symmetry in a four-dimensional U(1) gauge theory coupled to massless fermions with electromagnetic SL(2, Z) duality. This is done by deriving the AdlerBell-Jackiw anomaly of massless QED in the dual frame that is used to explicitly construct the symmetry defect operator as well as the conserved two-form symmetry current. As expected, the noninvertible chiral symmetry is covariant under the duality transformation. This has implications for understanding the nature of kinetic and topological terms in the dual frame and for axion electrodynamics. In particular, we show that to generate an axion potential from a dyon loop, the one-form magnetic symmetry must be explicitly broken by a mutually nonlocal charged state with nonzero pairwise helicity.

The kinetic mixing of two U(1) gauge theories can result in a massless photon that has perturbative couplings to both electric and magnetic charges. This framework can be used to perturbatively calculate in a quantum field theory with both kinds of charge. Here we reexamine the running of the magnetic charge, where the calculations of Schwinger and Coleman sharply disagree. We calculate the running of both electric and magnetic couplings and show that the disagreement between Schwinger and Coleman is due to an incomplete summation of topological terms in the perturbation series. We present a momentum space prescription for calculating the loop corrections in which the topological terms can be systematically separated for resummation. Somewhat in the spirit of modern amplitude methods we avoid using a vector potential and use the field strength itself, thereby trading gauge redundancy for the geometric redundancy of Stokes surfaces. The resulting running of the couplings demonstrates that Dirac charge quantization is independent of renormalization scale, as Coleman predicted. As a simple application we also bound the parameter space of magnetically charged states through the experimental measurement of the running of electromagnetic coupling.

We study representations of the Poincaré group that have a privileged transformation law along a p-dimensional hyperplane, and uncover their associated spinor-helicity variables in D spacetime dimensions. Our novel representations generalize the recently introduced celestial states and transform as conformal primaries of SO(p,1), the symmetry group of the p-hyperplane. We will refer to our generalized states as “partially celestial.” Following Wigner’s method, we find the induced representations, including spin degrees of freedom. Defining generalized spinor-helicity variables for every D and p, we are able to construct the little group covariant part of partially celestial amplitudes. Finally, we briefly examine the application of the pairwise little group to partially celestial states with mutually nonlocal charges. Published by the American Physical Society 2024

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,717 new measurements from 869 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Most of the 120 reviews are updated, including many that are heavily revised. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app.

It is usually assumed that 4D instantons can only arise in non-Abelian theories. In this paper we re-examine this conventional wisdom by explicitly constructing instantons in an Abelian gauge theory: QED_4 with N_f flavors of Dirac fermions, in the background of a Dirac monopole. This is the low-energy effective field theory for fermions interacting with a 't Hooft-Polyakov monopole, in the limit where the monopole is infinitely heavy (hence pointlike) and static. This theory, whose non-topological sectors were studied by Rubakov and Callan, has a far richer structure than previously explored. We show how to calculate the topological instanton number, demonstrate the existence of 't Hooft zero modes localized around such instantons, and show how instantons in the path integral provide the underlying mechanism for the Callan-Rubakov process: monopole-catalyzed baryon decay with a cross section that saturates the unitarity bound. Our computation relies on correctly identifying the relevant 2D EFT for monopole catalysis as Axial QED_2 in an effective AdS_2 metric.

We present a fully calculable UV complete toy model of a Peccei-Quinn (PQ) axion coupled to magnetic monopoles as well as electric charges. The theory has manifest electric-magnetic duality built in. We find that the axion-photon coupling contains the usual anomaly term, plus periodic corrections which can also become large if the monopole is light, without violating the discrete axion shift symmetry. These additional periodic terms can be identified as the non-perturbative corrections due to the monopoles (and other BPS states), but can also be interpreted as a sum over instanton corrections. The key aspect helping reconcile axion coupling quantization with electric-magnetic duality is the fact that the axion itself undergoes a non-linear transformation under electric-magnetic duality. The theory analyzed here is just the original $N=2$ supersymmetric $SU(2)$ Seiberg-Witten theory, which contains a PQ axion due to an anomalous spontaneously broken global $R$-symmetry, as well as massless fermionic monopoles and dyons at special points in the moduli space. Hence the entire machinery of the Seiberg-Witten solution can be applied to reliably calculate the photon-axion coupling in different duality frames. We show explicitly that the physically observable axion-photon amplitude is duality invariant, as it had to be.

The constructive method of determining amplitudes from on-shell pole structure has been shown to be promising for calculating amplitudes in a more efficient way. However, challenges have been encountered when a massless internal photon is involved in the gluing of three-point amplitudes with massive external particles. In this paper, we use the original on-shell method, old-fashioned perturbation theory, to shed light on the constructive method, and show that one can derive the Feynman amplitude by correctly identifying the residue even when there is an internal photon involved.

Abstract We construct the Faddeev-Kulish dressed multiparticle states of electrically and magnetically charged particles, incorporating the effects of real and virtual soft photons. We calculate the properties of such dressed states under Lorentz transformations, and find that they can be identified with the pairwise multi-particle states that transform under the pairwise little group. The shifts in the dressing factors under Lorentz transformations are finite and have a simple geometric interpretation. Using the transformation properties of the dressed states we also present a novel, fully quantum field theoretic derivation of the geometric (Berry) phase obtained by an adiabatic rotation of the Dirac string, and also of the Dirac quantization condition. For half integer pairwise helicity, we show that these multiparticle states have flipped spin-statistics, reproducing the surprising fact that fermions can be made out of bosons.

We study SU(5) SU(5) chiral gauge theories on R^3\times S^1 R3×S1 . With an unequal number of fundamental and antifundmental matter representations we calculate nontrivial pre-ADS superpotentials generated by composite multi-monopoles. We also point out that the structure of the composite multi-monopoles can be determined simply from the affine Dynkin diagrams of the gauge group and its unbroken subgroup. For the case of one flavor, we find that the superpotential is independent of the composite meson. We show that dynamical 4D SUSY breaking in the simplest chiral SU(5) SU(5) gauge theory can be demonstrated directly via semi-classical effects on the circle.

We study SU(5) chiral gauge theories on R(3)xS(1). With an unequal number of fundamental and antifundmental matter representations we calculate nontrivial pre-ADS superpotentials generated by composite multi-monopoles. We also point out that the structure of the composite multi-monopoles can be determined simply from the affine Dynkin diagrams of the gauge group and its unbroken subgroup. For the case of one flavor, we find that the superpotential is independent of the composite meson. We show that dynamical 4D SUSY breaking in the simplest chiral SU(5) gauge theory can be demonstrated directly via semi-classical effects on the circle.

We suggest a novel resolution for a decades old mystery-what happens when a positron scatters off a minimal grand-unification-theory monopole in an s wave, a puzzle first discussed by Callan in 1983. Using the language of on shell amplitudes and pairwise helicity we suggest that the final state contains two up quarks and a down quark in an entangled "pairwise" multiparticle state-the only particle final state that satisfies angular momentum and gauge charge conservation. The cross section for this process is as large as in the original Rubakov-Callan effect, only suppressed by the QCD scale. The final state we find cannot be seen in Callan's truncated 2D theory, since our new pairwise state appears only in more than two dimensions.

We extend the definition of asymptotic multiparticle states of the S-matrix beyond the tensor products of one-particle states. We identify new quantum numbers called pairwise helicities, or q_{ij}, associated with asymptotically separated pairs of particles. We first treat all single particles and particle pairs independently, allowing us to generalize the Wigner construction, and ultimately projecting onto the physical states. Our states reduce to tensor product states for vanishing q_{ij}, while for vanishing spins they reproduce Zwanziger's scalar dyon states. This construction yields the correct asymptotic states for the scattering of electric and magnetic charges, with pairwise helicity identified as q_{ij}=e_{i}g_{j}-e_{j}g_{i}.

On-shell methods are particularly suited for exploring the scattering of electrically and magnetically charged objects, for which there is no local and Lorentz invariant Lagrangian description. In this paper we show how to construct a Lorentz-invariant S-matrix for the scattering of electrically and magnetically charged particles, without ever having to refer to a Dirac string. A key ingredient is a revision of our fundamental understanding of multi-particle representations of the Poincar\'e group. Surprisingly, the asymptotic states for electric-magnetic scattering transform with an additional little group phase, associated with pairs of electrically and magnetically charged particles. The corresponding "pairwise helicity" is identified with the quantized "cross product" of charges, $e_1 g_2 - e_2 g_1$, for every charge-monopole pair, and represents the extra angular momentum stored in the asymptotic electromagnetic field. We define a new kind of pairwise spinor-helicity variable, which serves as an additional building block for electric-magnetic scattering amplitudes. We then construct the most general 3-point S-matrix elements, as well as the full partial wave decomposition for the $2\to 2$ fermion-monopole S-matrix. In particular, we derive the famous helicity flip in the lowest partial wave as a simple consequence of a generalized spin-helicity selection rule, as well as the full angular dependence for the higher partial waves. Our construction provides a significant new achievement for the on-shell program, succeeding where the Lagrangian description has so far failed.

We resolve the decades old mystery of what happens when a positron scatters off a minimal GUT monopole in an s-wave, first discussed by Callan in 1983. Using the language of on-shell amplitudes and pairwise helicity we show that the final state contains two up quarks and a down quark entangled with angular momentum stored in the gauge fields, which is the only particle final state that satisfies angular momentum and gauge charge conservation. The cross section for this process is as large as in the original Rubakov-Callan effect, only suppressed by the QCD scale. The final state we find cannot be seen in Callan's truncated 2D theory, since our entanglement requires more than 2 dimensions.

We examine distinctive signatures of Quantum Critical Higgs models at the LHC and future higher energy colliders. In these models the Higgs boson is part of a conformal sector that is softly broken at a threshold scale, and generically the scaling dimension of the Higgs is larger than in the Standard Model. In particular we examine the gg → H → ZZ, gg → H → γγ, and gg → Z → H Z channels to see how the cross sections deviate from the Standard Model in the high invariant mass region. In order to perform the calculations we use 5D duals of Quantum Critical Higgs models using the AdS/CFT correspondence, with a soft wall to break the conformal symmetry.

Theories with both electric and magnetic charges (“mutually non-local” theories) have several major obstacles to calculating scattering amplitudes. Even when the interaction arises through the kinetic mixing of two, otherwise independent, U(1)’s, so that all low-energy interactions are perturbative, difficulties remain: using a self-dual, local formalism leads to spurious poles at any finite order in perturbation theory. Correct calculations must show how the spurious poles cancel in observable scattering amplitudes. Consistency requires that one type of charge is confined as a result of one of the U(1)’s being broken. Here we show how the constraints of confinement and parity conservation on observable processes manages to cancel the spurious poles in scattering and pair production amplitudes, paving the way for systematic studies of the experimental signatures of “dark” electric-magnetic processes. Along the way we demonstrate some novel effects in electric-magnetic interactions, including that the amplitude for single photon production of magnetic particles by electric particles vanishes.

Continuum supersymmetry is a class of models in which the supersymmetric partners together with part of the standard model come from a conformal sector, broken in the IR near the TeV scale. Such models not only open new doors for addressing the problems of the standard model, but also have unique signatures at hadron colliders, which might explain why we have not yet seen any superpartners at the LHC. Here we use gaugegravity duality to model the conformal sector, generate collider simulations, and finally analyze continuum gluino signatures at the LHC. Due to the increase in the number of jets produced the bounds are weaker than for the minimal supersymmetric standard model with the same gluino mass threshold.