Standard Gauge Theory Research Articles

Fractons, symmetric gauge fields and geometry

Gapless fracton phases are characterized by the conservation of certain charges and their higher moments. These charges generically couple to higher rank gauge fields. In this paper we study systems conserving charge and dipole moment, and construct the corresponding gauge fields propagating in arbitrary curved backgrounds. The relation between the symmetries of these class of systems and spacetime transformations is discussed. In fact, we argue that higher rank symmetric gauge theories are closer to gravitational fields than to a standard gauge theory.

Scalar and vector gauges unification in de Sitter ambient space formalism

We consider the massless minimally coupled scalar field in the de Sitter ambient space formalism as a gauge potential or connection field. We construct the scalar gauge theory by helping an arbitrary constant five-vector field Bα analogous to the standard gauge theory. The Lagrangian density of the interaction between the scalar and spinor fields is presented in this framework. The Yukawa potential can be extracted from this Lagrangian density at the null curvature limit by an appropriate choice of a constant five-vector field. It is shown that the de Sitter ambient space formalism permits us to unify the scalar and vector gauge fields. By choosing a matrix form for the constant five-vector field Bα, the unification of scalar and vector gauge fields in the spectral action of noncommutative geometry can be rewritten. We discuss that if the scalar gauge field is considered as a conformal sector of the background metric field, it may be interpreted as the connection field between the different de Sitter hyperboloids in the quantum geometry from the classical point of view.

Clifford algebra from quantum automata and unitary Wilson fermions

We introduce a spacetime discretization of the Dirac equation that has the form of a quantum automaton and that is invariant upon changing the representation of the Clifford algebra, like the Dirac equation itself. Our derivation follows Dirac's original one: We required that the square of the discrete Dirac scheme be what we define as an acceptable discretization of the Klein-Gordon equation. In contrast to standard lattice gauge theory in discrete time, in which unitarity needs to be proven, we show that the quantum automaton delivers naturally unitary Wilson fermions for any choice of Wilson's parameter.

Angular momentum without rotation: Turbocharging relationalism

Rotation is a challenging riddle for the relationalist. In early versions of the absolute-relational debate for example, Newton’s rotating bucket poured cold water on the relationalist position. While the parameters of the debate have changed, a more recent analysis in 1999 by Belot proclaimed rotation to be “the downfall of relationalism.”In this paper, we provide a relational response to the riddle of rotation. We present a theory that, contrary to orthodoxy, can account for all rotational effects without introducing, as the absolutist does, a fixed standard of rotation. Instead, our theory posits a universal SO(3) charge that plays the role of global angular momentum and couples to inter-particle relations via terms commonly seen in standard gauge theories such as electromagnetism and the Standard Model of particle physics.Our theory makes use of an enriched form of relationalism: it adds an SO(3) structure to the traditional relational description. Our construction is made possible by the modern tools of gauge theory, which reveal a simple relational law describing rotational effects. In this way, we can save all the phenomena of Newtonian mechanics using conserved charges and relationalism. In a second paper, we will further explore the ontological and explanatory implications of the theory developed here.

Fresh perspective on gauging the conformal group

We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and the consequences of global conformal invariance for field theories, before reconsidering existing approaches for gauging the conformal group, namely auxiliary conformal gauge theory and biconformal gauge theory, neither of which is generally accepted as a complete solution. We then demonstrate that, provided any matter fields belong to an irreducible representation of the Lorentz group, the recently proposed extended Weyl gauge theory (eWGT) may be considered as an alternative method for gauging the conformal group, since eWGT is invariant under the full set of local conformal transformations, including inversions, as well as possessing conservation laws that provide a natural local generalisation of those satisfied by field theories with global conformal invariance, and also having an `ungauged' limit that corresponds to global conformal transformations. By contrast, although standard Weyl gauge theory also enjoys the first of these properties, it does not share the other two, and so cannot be considered a valid gauge theory of the conformal group.

The underlying geometry of the CAM gauge model of the Standard Model of particle physics

The Composition Algebra-based Methodology (CAM) [B. Wolk, Pap. Phys. 9, 090002 (2017); Phys. Scr. 94, 025301 (2019); Adv. Appl. Clifford Algebras 27, 3225 (2017); J. Appl. Math. Phys. 6, 1537 (2018); Phys. Scr. 94, 105301 (2019), Adv. Appl. Clifford Algebras 30, 4 (2020)], which provides a new model for generating the interactions of the Standard Model, is geometrically modeled for the electromagnetic and weak interactions on the parallelizable sphere operator fiber bundle [Formula: see text] consisting of base space, the tangent bundle [Formula: see text] of space–time [Formula: see text], projection operator [Formula: see text], the parallelizable spheres [Formula: see text] conceived as operator fibers [Formula: see text] attaching to and operating on [Formula: see text] [Formula: see text] as [Formula: see text] varies over [Formula: see text], and as structure group, the norm-preserving symmetry group [Formula: see text] for each of the division algebras which is simultaneously the isometry group of the associated unit sphere. The massless electroweak [Formula: see text] Lagrangian is shown to arise from [Formula: see text]’s generation of a local coupling operation on sections of Dirac spinor and Clifford algebra bundles over [Formula: see text]. Importantly, CAM is shown to be a new genre of gauge theory which subsumes Yang–Mills Standard Model gauge theory. Local gauge symmetry is shown to be at its core a geometric phenomenon inherent to CAM gauge theory. Lastly, the higher-dimensional, topological architecture which generates CAM from within a unified eleven [Formula: see text]-dimensional geometro-topological structure is introduced.

The Quantum Theory of the Lorentzian Fermionic Differential Forms

We consider the quantum theory of the Lorentzian fermionic differential forms and the corresponding bispinor quantum fields, which are expansion coefficients of the forms in the bispinor basis of Becher and Joos. We describe the canonical quantization procedure for the bispinor gauge theory in terms of its Dirac spinor constituents in detail and derive the corresponding Feynman rules and also all possible mass terms for massive fermions in the bispinor gauge theory. We classify the solutions by a scalar spin quantum number, a number with no analogue in the standard gauge theory and in the Standard Model. The possible mass terms correspond to combinations of scalar spin-zero singlets and scalar spin-1/2 doublets in the generation space. We describe the connection between the Lorentz spin of bispinors and the scalar spin of bispinor constituents.

Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks

Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with synthetic, external electromagnetic fields. One introduces this interaction as additional phases that play the role of gauge fields. Here, we present a way to incorporate those phases, which differs from previous works. Our proposal allows the discrete derivatives, that appear under a gauge transformation, to treat time and space on the same footing, in a way which is similar to standard lattice gauge theories. By considering two steps of the evolution, we define a density current which is gauge invariant and conserved. In the continuum limit, the dynamics of the particle, under a suitable choice of the parameters, becomes the Dirac equation, and the conserved current satisfies the corresponding conservation equation.

Tetrads in SU(3) × SU(2) × U(1) Yang–Mills geometrodynamics

The relationship between gauge and gravity amounts to understanding the underlying new geometrical local structures. These structures are new tetrads specially devised for Yang–Mills theories, Abelian and non-Abelian in four-dimensional Lorentzian curved spacetimes. In the present paper, a new tetrad is introduced for the Yang–Mills [Formula: see text] formulation. These new tetrads establish a link between local groups of gauge transformations and local groups of spacetime transformations that we previously called LB1 and LB2. New theorems are proved regarding isomorphisms between local internal [Formula: see text] groups and local tensor products of spacetime LB1 and LB2 groups of transformations. These new tetrads define at every point in spacetime two orthogonal planes that we called blades or planes one and two. These are the local planes of covariant diagonalization of the stress–energy tensor. These tetrads are gauge dependent. Tetrad local gauge transformations leave the tetrads inside the local original planes without leaving them. These local tetrad gauge transformations enable the possibility to connect local gauge groups Abelian or non-Abelian with local groups of tetrad transformations. On the local plane one, the Abelian group [Formula: see text] of gauge transformations was already proved to be isomorphic to the tetrad local group of transformations LB1, for example. LB1 is [Formula: see text] plus two different kinds of discrete transformations. On the local orthogonal plane two [Formula: see text] is isomorphic to LB2 which is just [Formula: see text]. That is, we proved that LB1 is isomorphic to [Formula: see text] which is a remarkable result since a noncompact group plus two discrete transformations is isomorphic to a compact group. These new tetrads have displayed manifestly and nontrivially the coupling between Yang–Mills fields and gravity. The new tetrads and the stress–energy tensor allow for the introduction of three new local gauge invariant objects. Using these new gauge invariant objects and in addition a new general local duality transformation, a new algorithm for the gauge invariant diagonalization of the Yang–Mills stress–energy tensor is developed as an application. This is a paper about grand Standard Model gauge theories — General Relativity gravity unification and grand group unification in four-dimensional curved Lorentzian spacetimes.

Correlation function diagnostics for type-I fracton phases

Fracton phases are recent entrants to the roster of topological phases in three dimensions. They are characterized by subextensively divergent topological degeneracy and excitations that are constrained to move along lower dimensional subspaces, including the eponymous fractons that are immobile in isolation. We develop correlation function diagnostics to characterize Type I fracton phases which build on their exhibiting {\it partial deconfinement}. These are inspired by similar diagnostics from standard gauge theories and utilize a generalized gauging procedure that links fracton phases to classical Ising models with subsystem symmetries. En route, we explicitly construct the spacetime partition function for the plaquette Ising model which, under such gauging, maps into the X-cube fracton topological phase. We numerically verify our results for this model via Monte Carlo calculations.

Finite quantum gauge theories

We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of running gauge coupling constant. The outcome is "a UV finite theory for any gauge interaction". Our calculations are done in D=4, but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite we are able to solve also the Landau pole problems, in particular in QED. Without any potential the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV, nor the singularities in the infrared regime (IR).

Finite volume corrections to the electromagnetic mass of composite particles

The long-range electromagnetic interaction presents a challenge for numerical computations in $\mathrm{QCD}+\mathrm{QED}$. In addition to power-law finite volume effects, the standard lattice gauge theory approach introduces nonlocality through removal of photon zero-momentum modes. The resulting finite volume effects must be quantitatively understood; and, to this end, nonrelativistic effective field theories are an efficient tool, especially in the case of composite particles. Recently an oddity related to nonlocality of the standard lattice approach was uncovered by the Budapest-Marseille-Wuppertal collaboration. Explicit contributions from antiparticles appear to be required so that finite volume QED results for a pointlike fermion can be reproduced in the effective field theory description. We provide transparency for this argument by considering pointlike scalars and spinors in finite volume QED using the method of regions. For the more germane case of composite particles, we determine that antiparticle modes contribute to the finite volume electromagnetic mass of composite spinors through terms proportional to the squares of timelike form factors evaluated at threshold. We extend existing finite volume calculations to one order higher, which is particularly relevant for the electromagnetic mass of light nuclei. Additionally, we verify that the analogous finite volume contributions to the nucleon mass in chiral perturbation theory vanish in accordance with locality.

D-brane on Poisson manifold and generalized geometry

The properties of the D-brane fluctuations are investigated using the two types of deformation of the Dirac structure, based on the B-transformation and the β-transformation, respectively. The former gives the standard gauge theory with two-form field strength. The latter gives a nonstandard gauge theory on the Poisson manifold with bivector field strength and the vector field as a gauge potential, where the gauge symmetry is a diffeomorphism generated by the Hamiltonian vector field. The map between the two gauge theories is also constructed with the help of Moser's Lemma and the Magnus expansion. We also investigate the relation to the gauge theory on the noncommutative D-branes.

Noncommutative teleparallel gravity from a consistent deformation of gauge theory

Starting from a standard noncommutative gauge theory and using the Seiberg-Witten map we propose a new version of a noncommutative gravity. We use consistent deformation theory starting from a free gauge action and gauging a killing symmetry of the background metric to construct a deformation of the gauge theory that we can relate with gravity. The result of this consistent deformation of the gauge theory is nonpolynomial in Aμ. From here we can construct a version of noncommutative gravity that is simpler than previous attempts. Our proposal is consistent and is not plagued with the problems of other approaches like twist symmetries or gauging other groups.

Holonomy spin foam models: Definition and coarse graining

We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbitrary two-complexes as well as to generalize current spin foam models to arbitrary, in particular finite groups. The similarity with standard lattice gauge theories allows to apply standard coarse graining methods, which for finite groups can now be easily considered numerically. We will summarize other holonomy and spin network formulations of spin foams and group field theories and explain how the different representations arise through variable transformations in the partition function. A companion paper will provide a description of boundary Hilbert spaces as well as a canonical dynamic encoded in transfer operators.

Anomalous molecular dynamics in the vicinity of a conical intersection

Conical intersections between molecular electronic potential energy surfaces can greatly affect molecular dynamics and chemical properties. Molecular gauge theory is capable of explaining many of these often unexpected phenomena deriving from the physics of the conical intersection. Here we will give an example of anomalous dynamics in the paradigm E × ϵ Jahn-Teller model, which does not allow for a simple explanation in terms of standard molecular gauge theory. By introducing a dual gauge theory, we unwind this surprising behavior by identifying it with an intrinsic spin Hall effect. Thus, this work link knowledge of condensed-matter theories with non-adiabatic molecular dynamics. Furthermore, via ab initio calculations of potential energy surfaces, the findings are as well demonstrated to appear in a realistic system such as the Li3 molecule.

Gauge-Higgs Unification Models in Six Dimensions withS2/Z2Extra Space and GUT Gauge Symmetry

We review gauge-Higgs unification models based on gauge theories defined on six-dimensional spacetime withS2/Z2topology in the extra spatial dimensions. Nontrivial boundary conditions are imposed on the extraS2/Z2space. This review considers two scenarios for constructing a four-dimensional theory from the six-dimensional model. One scheme utilizes the SO(12) gauge symmetry with a special symmetry condition imposed on the gauge field, whereas the other employs the E6gauge symmetry without requiring the additional symmetry condition. Both models lead to a standard model-like gauge theory with theSU(3)×SU(2)L×U(1)Y(×U(1)2)symmetry and SM fermions in four dimensions. The Higgs sector of the model is also analyzed. The electroweak symmetry breaking can be realized, and the weak gauge boson and Higgs boson masses are obtained.

Emergent noncommutative gravity from a consistent deformation of gauge theory

Starting from a standard noncommutative gauge theory and using the Seiberg-Witten map we propose a new version of a noncommutative gravity. We use consistent deformation theory starting from a free gauge action and gauging a killing symmetry of the background metric to construct a deformation of the gauge theory that we can relate with gravity. The result of this consistent deformation of the gauge theory is nonpolynomial in A_\mu. From here we can construct a version of noncommutative gravity that is simpler than previous attempts. Our proposal is consistent and is not plagued with the problems of other approaches like twist symmetries or gauging other groups.

Holomorphic Corrections from Wrapped Euclidean Branes

We discuss how non-perturbative corrections to the four-dimensional effective superpotential are generated by wrapped Euclidean D-branes. It is shown how such terms can be computed and we give a few examples of holomorphic couplings that arise front a D-brane instanton effect in string theory. Some of these instanton configurations give rise to phenomenologically desirable couplings although they do not admit an obvious interpretation in terms of standard gauge theory.

Local Poincaré Symmetry in Gauge Theory of Gravity

It is well known that the Poincaré gauge theories of gravity do not have the structure of a standard gauge theory. Nevertheless, we show that a general form of action for the gravitational gauge fields in the gauge theory does possess local Poincaré invariance.