Gauge Field Theory Research Articles

Duality symmetry of quantum electrodynamics and magnetic charges

The duality symmetry between electricity and magnetism hidden in classical Maxwell equations suggests the existence of dual charges, which have usually been interpreted as magnetic charges and have not been observed in experiments. In quantum electrodynamics (QED), the electric and magnetic fields are unified into a single gauge field, which makes this symmetry inconspicuous. Here, we revisit the duality symmetry of QED by introducing a dual gauge field and a dual symmetric Lagrangian. Within the framework of gauge-field theory, we show that the electric–magnetic duality symmetry cannot give any new conservation law. By checking the charge–charge interaction and the quantum Lorentz-force equation, we find that the introduced dual charges are electric charges, not magnetic charges. Notably, we show that genuine magnetic charges are incompatible with the traditional QED gauge-field framework, as the interaction between a magnetic charge and an electric charge cannot be mediated via the exchange of gauge photons.

Finite presentations for stated skein algebras and lattice gauge field theory

Finite presentations for stated skein algebras and lattice gauge field theory

Notes on the L∞-approach to local gauge field theories

It is well known that a Q-manifold gives rise to an L∞-algebra structure on the tangent space at a fixed point of the homological vector field. From the field theory perspective this implies that the expansion of a classical Batalin-Vilkovisky (BV) formulation around a vacuum solution can be equivalently cast into the form of an L∞-algebra. In so doing, the BV symplectic structure determines a compatible cyclic structure on the L∞-algebra. Moreover, L∞ quasi-isomorphisms correspond to so-called equivalent reductions (also known as the elimination of generalized auxiliary fields) of the respective BV systems. Although at the formal level the relation is straightforward, its implementation in field theory requires some care because the underlying spaces become infinite-dimensional. In the case of local gauge theories, the relevant spaces can be approximated by nearly finite-dimensional ones through employing the jet-bundle technique. In this work we study the L∞-counterpart of the jet-bundle BV approach and generalise it to a more flexible setup of so-called gauge PDEs. It turns out that in the latter case the underlying L∞-structure is analogous to that of Chern-Simons theory. In particular, the underlying linear space is a module over the space-time exterior algebra and the higher L∞-maps are multilinear. Furthermore, a counterpart of the cyclic structure turns out to be degenerate and possibly nonlinear, and corresponds to a compatible presymplectic structure the gauge PDE, which is known to encode the BV symplectic structure and hence the full-scale Lagrangian BV formulation. Moreover, given a degenerate cyclic structure one can consistently relax the L∞-axioms in such a way that the formalism still describes non-topological models but involves only finitely-generated modules, as we illustrate in the example of Yang-Mills theory.

Noncommutative $$SO(2,3)_{\star }$$ gauge theory of gravity

Topological gravity (in the sense that it is metric-independent) in a 2n-dimensional spacetime can be formulated as a gauge field theory for the AdS gauge group $$SO(2,2n-1)$$ by adding a multiplet of scalar fields. These scalars can break the gauge invariance of the topological gravity action, thus making a connection with Einstein’s gravity. This review is about a noncommutative (NC) star-product deformation of the four-dimensional AdS gauge theory of gravity, including Dirac spinors and the Yang–Mills field. In general, NC actions can be expanded in powers of the canonical noncommutativity parameter $$\theta$$ using the Seiberg–Witten map. The leading-order term of the expansion is the classical action, while the higher-order $$\theta$$ -dependent terms are interpreted as new types of coupling between classical fields due to spacetime noncommutativity. We study how these perturbative NC corrections affect the field equations of motion and derive some phenomenological consequences, such as NC-deformed Landau levels of an electron. Finally, we discuss how topological gravity in four dimensions (both classical and noncommutative) appears as a low-energy sector of five-dimensional Chern–Simons gauge theory in the sense of Kaluza–Klein reduction.

A statistical mechanical model for non-perturbative regimes

Thanks to Feynman graphons, as mathematical tools in dealing with Dyson–Schwinger equations, we formulate a new statistical mechanical model for the study of equilibrium states and observables associated with the solution space of quantum motions in a strongly coupled gauge field theory underlying the evolution of running coupling constants, time and temperature.

Lifting Bratteli diagrams between Krajewski diagrams: Spectral triples, spectral actions, and AF algebras

In this paper, we present a framework to construct sequences of spectral triples on top of an inductive sequence defining an $AF$-algebra. One aim of this paper is to lift arrows of a Bratteli diagram to arrows between Krajewski diagrams. The spectral actions defining Non-commutative Gauge Field Theories associated to two spectral triples related by these arrows are compared (tensored by a commutative spectral triple to put us in the context of Almost Commutative manifolds). This paper is a follow up of a previous one in which this program was defined and physically illustrated in the framework of the derivation-based differential calculus, but the present paper focuses more on the mathematical structure without trying to study the physical implications.

Dynamical Gauge Fields with Bosonic Codes.

The quantum simulation of dynamical gauge field theories offers the opportunity to study complex high-energy physics with controllable low-energy devices. For quantum computation, bosonic codes promise robust error correction that exploits multiparticle redundancy in bosons. Here, we demonstrate how bosonic codes can be used to simulate dynamical gauge fields. We encode both matter and dynamical gauge fields in a network of resonators that are coupled via three-wave mixing. The mapping to a Z_{2} dynamical lattice gauge theory is established when the gauge resonators operate as Schrödinger cat states. We explore the optimal conditions under which the system preserves the required gauge symmetries. Our findings promote realizing high-energy models using bosonic codes.

Gauging Fractons and Linearized Gravity

We consider the covariant gauge field theory of fractons, which describes a new type of quasiparticles exhibiting novel and non-trivial properties. In particular, we focus on the field theoretical peculiarities which characterize this theory, starting from the fact that, if we accept the paradigm that quantum field theories are defined by their symmetries, fractons unavoidably come together with linearized gravity. The standard Faddeev–Popov procedure to gauge fix the theory leads to a scalar gauge condition, which has two important drawbacks: it is frozen in the Landau gauge and linearized gravity cannot be obtained as a limit. In this paper, we adopt a tensorially alternative gauge fixing, which avoids both problems. In particular, this allows to show that important physical features, such as counting of the degrees of freedom, do not depend on a particular gauge choice, as expected. Moreover, the resulting gauge fixed theory contains both fractons and linearized gravity as a limit, differently from the standard scalar choice.

Non-invertible defects in 5d, boundaries and holography

We show that very simple theories of abelian gauge fields with a cubic Chern-Simons term in 5d have an infinite number of non-invertible codimension two defects. They arise by dressing the symmetry operators of the broken electric 1-form symmetry with a suitable topological field theory, for any rational angle. We further discuss the same theories in the presence of a 4d boundary, and more particularly in a holographic setting. There we find that the bulk defects, when pushed to the boundary, have various different fates. Most notably, they can become codimension one non-invertible defects of a boundary theory with an ABJ anomaly.

Quantum spin liquids

A glance at recent research on magnetism turns up a curious set of articles discussing, or claiming evidence for, a state of matter called a quantum spin liquid (QSL). These articles are notable in their invocation of exotic notions of topological physics, quantum entanglement, fractional quantum numbers, anyon statistics and gauge field theories. So what is a QSL and why do we need this complicated technical vocabulary to describe it? Our aim in this article is to introduce some of these concepts and provide a discussion of what a QSL is, where it might occur in Nature and why it is of interest. As we'll see, this is a rich subject which is still in development, and unambiguous evidence for the realisation of the QSL state in a magnetic material remains hotly debated. However, the payoff in terms of the special nature of quantum entanglement in the QSL, and its diverse spectrum of unusual excitations and topological status will (at least to some extent) justify the need to engage with some powerful, occasionally abstract, technical material.

Interactions of particles with “continuous spin” fields

Powerful general arguments allow only a few families of long-range interactions, exemplified by gauge field theories of electromagnetism and gravity. However, all of these arguments presuppose that massless fields have zero spin scale (Casimir invariant) and hence exactly boost invariant helicity. This misses the most general behavior compatible with Lorentz symmetry. We present a Lagrangian formalism describing interactions of matter particles with bosonic “continuous spin” fields with arbitrary spin scale ρ. Remarkably, physical observables are well approximated by familiar theories at frequencies larger than ρ, with calculable deviations at low frequencies and long distances. For example, we predict specific ρ-dependent modifications to the Lorentz force law and the Larmor formula, which lay the foundation for experimental tests of the photon’s spin scale. We also reproduce known soft radiation emission amplitudes for nonzero ρ. The particles’ effective matter currents are not fully localized to their worldlines when ρ ≠ 0, which motivates investigation of manifestly local completions of our theory. Our results also motivate the development of continuous spin analogues of gravity and non-Abelian gauge theories. Given the correspondence with familiar gauge theory in the small ρ limit, we conjecture that continuous spin particles may in fact mediate known long-range forces, with testable consequences.

Multi-messenger constraints on Abelian-Higgs cosmic string networks

Nielsen-Olesen vortices in the Abelian-Higgs (AH) model are the simplest realisations of cosmic strings in a gauge field theory. Large-scale numerical solutions show that the dominant decay channel of a network of AH strings produced from random initial conditions is classical field radiation. However, they also show that with special initial conditions, loops of string can be created for which classical field radiation is suppressed, and which behave like Nambu-Goto (NG) strings with a dominant decay channel into gravitational radiation. This indicates that cosmic strings are generically sources of both high-energy particles and gravitational waves. Here we adopt a simple parametrisation of the AH string network allowing for both particle and gravitational wave production. With a reference to a specific model for NG-like loop distribution, this sets the basis for a “multi-messenger” investigation of this model. We find that, in order to explain the NANOGrav detection of a possible gravitational wave background, while satisfying the constraint on NG-like loop production from simulations and bounds from the cosmic microwave background, the tension of the AH string in Planck units Gμ and the fraction of the NG-like loops f NG should satisfy Gμ f NG 2.6 ≳ 3.2 × 10-13 at 95% confidence. On the other hand, for such string tensions, constraints from the diffuse gamma-ray background (DGRB) indicate that more than 97% of the total network energy should be converted to dark matter (DM) or dark radiation. We also consider joint constraints on the annihilation cross-section, the mass, and the relic abundance of DM produced by decays of strings. For example, for a DM mass of 500 GeV, the observed relic abundance can be explained by decaying AH strings that also account for the NANOGrav signal.

Finite-group gauge theories on lattices as Hamiltonian systems with constraints

In this work, we present a brief but insightful overview of the gauge theories, which are defined on n-dimensional lattices by using finite gauge groups, in order to show how they can be interpreted as a Hamiltonian system with constraints, analogous to what happens with the classical (continuous) gauge (field) theories. As this interpretation is not usually explored in the literature that discusses/introduces the concept of lattice gauge theory, but some recent works have been exploring Hamiltonian models in order to support some kind of quantum computation, we use this interpretation to, for example, present a brief geometric view of one class of these models: the Kitaev Quantum Double Models.

Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit

It has been observed that when the gauge fields are present on the link, fermion propagation is possible in the weak coupling limit due to the dominance of the hopping term, which corresponds to the colour gauge interaction in the lattice QCD formulation. The production of low energy skyrmionic excitation at the fermionic site destroys the underlying antiferromagnetic order. In the continuum limit, the kinetic term in the lattice QCD corresponds to the rearrangement of the fermionic constituents through their propagation within the confined domain of the bound stateconfigurations of the interacting system which gives rise to a running coupling constant leading to asymptotic freedom. When one can assign a colour to a particular quantum number of a fermionic component in a limited state, it shows that QCD may be thought of as a generalised non-Abelian gauge field theory since these degrees of freedom play a part in the restricted area of the system and examines the continuous limit of the Hubbard-like model and the weak coupling limit that results from the abolition of the antiferromagnetic order and fermion propagation. This is equivalent to the non-Abelian color gauge field interaction. It is noted that the generalised spin fluctuation may be linked to the colour gauge field. This formalism's discovery of pseudoscalar Goldstone bosons associated with chiral symmetry breaking is in line with (3+1)D continuum QCD.

Properties of the conformal Yangian in scalar and gauge field theories

Properties of the SO(2, n) Yangian acting on scalar and gauge fields are presented. This differential operator representation of the infinite-dimensional extension of the conformal algebra SO(2, n) is proved to satisfy the Serre relation for arbitrary spacetime dimension n for off-shell scalar theory, but only on shell and for n = 4 in the gauge theory. The SO(2, n) Yangian acts simply on the off-shell kinematic invariants (kI + kI+1 + …)2, and it annihilates individual off-shell scalar λϕ3 Feynman tree graphs for n = 6 if the differential operator representation is extended by graph dependent evaluation terms. The SO(2, 4) Yangian level one generators are shown to act in a compact way on pure Yang- Mills gluon tree amplitudes. The action of the Yangian on the scattering polynomials of a CHY formalism is also described.

Conserved currents for the gauge-field theory with Lorentz symmetry group and a composite theory of gravity

For the Yang-Mills–type gauge-field theory with Lorentz symmetry group, we propose and verify an explicit expression for the conserved currents in terms of the energy-momentum tensor. A crucial ingredient is the assumption that the gauge symmetry arises from the decomposition of a metric in terms of tetrad variables. The currents exist under the weak condition that the energy-momentum tensor and the Ricci tensor commute. We show how the conserved currents can be used to obtain a composite theory of gravity and discuss the static isotropic field around a point mass at rest.

Palatini formulation for gauge theory: implications for slow-roll inflation

We consider a formulation of gauge field theory where the gauge field $A_\alpha$ and the field strength $F_{\alpha\beta}$ are independent variables, as in the Palatini formulation of gravity. For the simplest gauge field action, this is known to be equivalent to the usual formulation. We add non-minimal couplings between $F_{\alpha\beta}$ and a scalar field, solve for $F_{\alpha\beta}$ and insert it back into the action. This leads to modified gauge field and scalar field terms. We consider slow-roll inflation and show that because of the modifications to the scalar sector, adding higher order terms to the inflaton potential does not spoil its flatness, unlike in the usual case. Instead they make the effective potential closer to quadratic. The modifications also solve the problem that Higgs inflation in the Palatini formulation is sensitive to higher order terms.

Palatini formulation for gauge theory: implications for slow-roll inflation

We consider a formulation of gauge field theory where the gauge field $A_\alpha$ and the field strength $F_{\alpha\beta}$ are independent variables, as in the Palatini formulation of gravity. For the simplest gauge field action, this is known to be equivalent to the usual formulation. We add non-minimal couplings between $F_{\alpha\beta}$ and a scalar field, solve for $F_{\alpha\beta}$ and insert it back into the action. This leads to modified gauge field and scalar field terms. We consider slow-roll inflation and show that because of the modifications to the scalar sector, adding higher order terms to the inflaton potential does not spoil its flatness, unlike in the usual case. Instead they make the effective potential closer to quadratic. The modifications also solve the problem that Higgs inflation in the Palatini formulation is sensitive to higher order terms.

Principal bundles and connections modelled by Lie group bundles

In this work, generalized principal bundles modelled by Lie group bundle actions are investigated. In particular, the definition of equivariant connections in these bundles, associated to Lie group bundle connections, is provided, together with the analysis of their existence and their main properties. The final part gives some examples. In particular, since this research was initially originated by some problems on geometric reduction of gauge field theories, we revisit the classical Utiyama Theorem from the perspective investigated in the article.

Entanglement structures in quantum field theories: Negativity cores and bound entanglement in the vacuum

The many-body entanglement between two finite (size-$d$) disjoint vacuum regions of noninteracting lattice scalar field theory in one spatial dimension, i.e., a ${({d}_{A}\ifmmode\times\else\texttimes\fi{}{d}_{B})}_{\mathrm{mixed}}$ Gaussian continuous variable system, is locally transformed into a tensor-product core of ${({1}_{A}\ifmmode\times\else\texttimes\fi{}{1}_{B})}_{\mathrm{mixed}}$ entangled pairs. Accessible entanglement within these core pairs exhibits an exponential hierarchy and as such identifies the structure of dominant region modes from which vacuum entanglement could be extracted into a spatially separated pair of quantum detectors. Beyond the core, the remaining modes of the halo are determined to be $AB$ separable in isolation, as well as separable from the core. However, state preparation protocols that distribute entanglement in the form of ${({1}_{A}\ifmmode\times\else\texttimes\fi{}{1}_{B})}_{\mathrm{mixed}}$ core pairs are found to require additional entanglement in the halo that is obscured by classical correlations. This inaccessible (bound) halo entanglement is found to mirror the accessible entanglement, but with a step behavior as the continuum is approached. It remains possible that alternate initialization protocols that do not utilize the exponential hierarchy of core-pair entanglement may require less inaccessible entanglement. Entanglement consolidation is expected to persist in higher dimensions and may aid classical and quantum simulations of asymptotically free gauge field theories, such as quantum chromodynamics.