Order Gauge Field Research Articles

Emergent (2+1)D topological orders from iterative (1+1)D gauging

Gauging introduces gauge fields in order to localize an existing global symmetry, resulting in a dual global symmetry on the gauge fields that can be gauged again. By iterating the gauging process on spin chains with Abelian group symmetries and arranging the gauge fields in a 2D lattice, the local symmetries become the stabilizer of the XZZX-code for any Abelian group. By twisting the gauging map, we obtain codes that explicitly confine anyons, whose local creating operators violate an odd number of plaquettes. Their fusion results in either mobile dipole excitations twisting only half of the plaquette terms, or complete immobile Sierpiński-like excitations if we twist all the terms. Our construction naturally realizes any gapped boundary by taking different quantum phases of the initial (1+1)D globally symmetric system. In addition, our method also establishes a promising route to obtain higherdimensional topological codes from lower ones and to identify their gapped boundaries and their tensor network representations.

Higgs inflation at the pole

We propose a novel possibility for Higgs inflation where the perturbative unitarity below the Planck scale is ensured by construction and the successful predictions for inflation are accommodated. The conformal gravity coupling for the Higgs field leads to the proximity of the effective Planck mass to zero in the Jordan frame during inflation, corresponding to a pole in the Higgs kinetic term in the Einstein frame. Requiring the Higgs potential to vanish at the conformal pole in the effective theory in the Jordan frame, we make a robust prediction of the successful Higgs inflation. For a successful Higgs inflation at the pole, we take the running quartic coupling for the Higgs field to be small enough at the inflation scale, being consistent with the low-energy data, but we need a nontrivial extension of the SM with extra scalar or gauge fields in order to keep the running Higgs quartic coupling small during inflation. Performing the perturbative analysis of reheating with the known couplings of the SM particles to the Higgs boson, we show that a concrete realization of the Higgs pole inflation can be pinned down by the reheating processes with a general equation of state for the Higgs inflaton. We illustrate some extensions of the simple Higgs pole inflation to the general pole expansions, the running Higgs quartic coupling in the Standard Model and its extension with a singlet scalar field, a supergravity embedding of the Higgs pole inflation.

Generalized U(N) gauge transformations in the realm of the extended covariant Hamilton formalism of field theory

The Lagrangians and Hamiltonians of classical field theory require to comprise gauge fields in order to be form-invariant under local gauge transformations. These gauge fields have turned out to correctly describe pertaining elementary particle interactions. In this paper, this principle is extended to require additionally the form-invariance of a classical field theory Hamiltonian under variations of the space-time curvature emerging from the gauge fields. This approach is devised on the basis of the extended canonical transformation formalism of classical field theory which allows for transformations of the space-time metric in addition to transformations of the fields. Working out the Hamiltonian that is form-invariant under extended local gauge transformations, we can dismiss the conventional requirement for gauge bosons to be massless in order for them to preserve the local gauge invariance. The emerging equation of motion for the curvature scalar R turns out to be compatible with that from a Proca system in the case of a static gauge field.Communicated by H Stöcker

Fictitious gauge fields in bilayer graphene

We discuss the effect of elastic deformations on the electronic properties of bilayer graphene membranes. Distortions of the lattice translate into fictitious gauge fields in the electronic Dirac Hamiltonian which are explicitly derived here for arbitrary elastic deformations. We include gauge fields associated to intra- as well as inter-layer hopping terms and discuss their effects in different contexts. As a first application, we use the gauge fields in order to study the recently predicted strain-induced Lifshitz transition for the Fermi surface at low energy. As a second application, we discuss the electron-phonon coupling induced by the fictitious gauge fields and analyse its contribution to the electrical resistivity of suspended bilayer membranes. Of special interest is the appearance of a linear coupling for flexural modes, in stark contrast to the case of monolayer graphene. This new coupling channel is shown to dominate the temperature-dependent resistivity in suspended samples with low tension.

Gauge formulation of general relativity using conformal and spin symmetries

The gauge symmetry inherent in Maxwell's electromagnetics has a profound impact on modern physics. Following the successful quantization of electromagnetics and other higher order gauge field theories, the gauge principle has been applied in various forms to quantize gravity. A notable development in this direction is loop quantum gravity based on the spin-gauge treatment. This paper considers a further incorporation of the conformal gauge symmetry in canonical general relativity. This is a new conformal decomposition in that it is applied to simplify recently formulated parameter-free construction of spin-gauge variables for gravity. The resulting framework preserves many main features of the existing canonical framework for loop quantum gravity regarding the spin network representation and Thiemann's regularization. However, the Barbero-Immirzi parameter is converted into the conformal factor as a canonical variable. It behaves like a scalar field but is somehow non-dynamical since the Hamiltonian constraint does not depend on its momentum. The essential steps of the mathematical derivation of this parameter-free framework for the spin-gauge variables of gravity are spelled out. The implications for the loop quantum gravity programme are briefly discussed.

Einstein-Yang-Mills solutions in higher dimensional de Sitter spacetime

We consider particlelike and black hole solutions of the Einstein-Yang-Mills system with positive cosmological constant in d>4 spacetime dimensions. These configurations are spherically symmetric and present a cosmological horizon for a finite value of the radial coordinate, approaching asymptotically the de Sitter background. In the usual Yang-Mills case, we find that the mass of these solutions, evaluated outside the cosmological horizon at future/past infinity, generically diverges for d>4. Solutions with finite mass are found by adding to the action higher order gauge field terms belonging to the Yang-Mills hierarchy. A discussion of the main properties of these solutions and their differences from those of the usual Yang-Mills model, both in four and higher dimensions, is presented.

Superfield algorithm for higher order gauge field theories

We propose an algorithm for the construction of higher order gauge field theories from a superfield formulation within the Batalin-Vilkovisky formalism. This is a generalization of the superfield algorithm recently considered by Batalin and Marnelius. This generalization seems to allow for non-topological gauge field theories as well as alternative representations of topological ones. A five dimensional non-abelian Chern-Simons theory and a topological Yang-Mills theory are treated as examples.

First order gauge field theories from a superfield formulation

Recently, Batalin and Marnelius proposed a superfield algorithm for master actions in the BV-formulation for a class of first order gauge field theories. Possible theories are determined by a ghost number prescription and a simple local master equation. We investigate consistent solutions of these local master equations with emphasis on four and six dimensional theories.

The pinch technique beyond one loop: the gauge-independent two-loop quark self-energy

It is shown how the pinch technique algorithm may be consistently extended beyond the one-loop level to obtain the gauge-independent two-loop fermion self-energy −i Σ (2) (p) in QCD in the pinch technique approach. The starting point for the construction is the general diagrammatic representation of the two-loop quark self-energy in terms of renormalized one-loop two- and three-point function and tree level Bethe-Salpeter-type quark-gluon scattering kernel insertions in the one-loop quark self-energy. Using factors of longitudinal gluon four-momentum only from lowest order gauge field propagators and triple gauge vertices to trigger the relevant Ward identities, the function − Σ (2) (p) is explicitly constructed from the consideration of the two-loop QCD corrections to the Compton scattering of a photon off a quark. It is shown that the resulting pinch technique self-energy − Σ (2) (p) is gauge-independent at all momenta, does not shift the position of the propagator pole and is multiplicatively renormalizable by local counterterms. The demonstration of the gauge independence is based on an efficient diagrammatic method to deal with the several dozen two-loop diagrams involved. It is explicitly shown by this example that the general correspondence between the pinch technique n-point functions and those obtained in the background field method in the Feynman quantum gauge ξ Q = 1 does not persist beyond one loop.

Influence of gauge-field fluctuations on composite fermions near the half-filled state.

Taking into account the transverse gauge field fluctuations, which interact with composite fermions, we examine the finite temperature compressibility of the fermions as a function of an effective magnetic field $\Delta B = B - 2 n_e hc/e$ ($n_e$ is the density of electrons) near the half-filled state. It is shown that, after including the lowest order gauge field correction, the compressibility goes as ${\partial n \over \partial \mu} \propto e^{- \Delta \omega_c / 2 T} \left ( 1 + {A (\eta) \over \eta - 1} {(\Delta \omega_c)^{2 \over 1 + \eta} \over T} \right )$ for $T \ll \Delta \omega_c$, where $\Delta \omega_c = {e \Delta B \over mc}$. Here we assume that the interaction between the fermions is given by $v ({\bf q}) = V_0 / q^{2 - \eta} \ (1 \le \eta \le 2)$, where $A (\eta)$ is a $\eta$ dependent constant. This result can be interpreted as a divergent correction to the activation energy gap and is consistent with the divergent renormalization of the effective mass of the composite fermions.

Topological Landau-Ginzburg theory for vortices in superfluid 4He.

We propose a modified Landau-Ginzburg theory for arbitrarily shaped vortex strings in superfluid $^{4}\mathrm{He}$. The theory contains a topological term and directly describes vortex dynamics. We introduce gauge fields in order to remove singularities from the Landau-Ginzburg order parameter of the superfluid, so that two kinds of gauge symmetries appear, making the continuity equation and conservation of the total vorticity manifest. The topological term gives rise to the Berry phase term in the vortex mechanical actions.

GAUGE-INVARIANT QUANTISATION OF CHIRAL GAUGE THEORIES

The path-integral functional of chiral gauge theories with background gauge potentials are derived in the holomorphic representation. Justification is provided, from first quantum mechanical principles, for the appearance of a functional phase factor of the gauge fields in order to maintain the gauge invariance. This term is shown to originate either from the Berry phase of the first-quantized hamiltonians or from the normal ordering of the second-quantized hamiltonian with respect to the Dirac in-vacuum. The quantization of the chiral Schwinger model is taken as an example.