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DOE OSTI2018

When rational sections become cyclic — Gauge enhancement in F-theory via Mordell-Weil torsion

We explore novel gauge enhancements from abelian to non-simply-connected gauge groups in F-theory. Accordingly, we consider complex structure deformations of elliptic fibrations with a Mordell-Weil group of rank one and identify the conditions under which the generating section becomes torsional. In the specific case of Ζ 2 torsion we construct the generic solution to these conditions and show that the associated F-theory compactification exhibits the global gauge group [SU (2) × SU (4) ]/Ζ 2 × SU (2) . The subsolution with gauge group SU (2) /Ζ 2 × SU (2) , for which we provide a global resolution, is related by a further complex structure deformation to a genus-one fibration with a bisection whose Jacobian has a Ζ 2 torsional section. While an analysis of the spectrum on the Jacobian fibration reveals an SU (2) /Ζ 2 × Ζ 2 gauge theory, reproducing this result from the bisection geometry raises some conceptual puzzles about F-theory on genus-one fibrations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Shadow sectors of gauge theories

We show that both abelian and non-abelian gauge theories admit configurations in which the fields behave as if in the presence of static charge densities, or “shadow charges”. These correspond to nontrivial initial conditions for the fields that generate gauge transformations, the Gauss’ law operators. In non-abelian theories, such configurations seem to demand additional physical fields with exactly static charge densities. In contrast with this expectation, we show that gauge theory alone provides a consistent and gauge-invariant description of shadow charges. Canonical quantization then yields continuous shadow charges for abelian theories and quantized ones for non-abelian theories. In general, our findings indicate that all local conservation laws give rise to gauge symmetries, even in the presence of second-class constraints.

Del Grosso, Loris [Johns Hopkins U.] (ORCID:000000↗

DOE OSTI2024

Noncommutative gauge symmetry in the fractional quantum Hall effect

Abstract We show that a system of particles on the lowest Landau level can be coupled to a probe U(1) gauge field$$ \mathcal{A} $$ A μ in such a way that the theory is invariant under a noncommutative U(1) gauge symmetry. While the temporal component$$ \mathcal{A} $$ A 0 of the probe field is coupled to the projected density operator, the spatial components$$ \mathcal{A} $$ A i are best interpreted as quantum displacements, which distort the interaction potential between the particles. We develop a Seiberg-Witten-type map from the noncommutative U(1) gauge symmetry to a simpler version, which we call “baby noncommutative” gauge symmetry, where the Moyal brackets are replaced by the Poisson brackets. The latter symmetry group is isomorphic to the group of volume preserving diffeomorphisms. By using this map, we resolve the apparent contradiction between the noncommutative gauge symmetry, on the one hand, and the particle-hole symmetry of the half-filled Landau level and the presence of the mixed Chern-Simons terms in the effective Lagrangian of the fractional quantum Hall states, on the other hand. We outline the general procedure which can be used to write down effective field theories which respect the noncommutative U(1) symmetry.

Physics↗

DOE OSTI2013

Quantization of gauge fields, graph polynomials and graph homology

We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology. -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge

A study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2) and for different Euclidean space–time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: (i) the finite Euclidean Yang–Mills action, (ii) the finite Hilbert norm. -- Highlights: •We study the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge. •For d=2 we obtain solutions with finite action but not finite Hilbert norm. •For d=3,4 we obtain solutions with finite action and finite Hilbert norm. •These results can be compared with those previously obtained in the Landau gauge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Gauge turbulence, topological defect dynamics, and condensation in Higgs models

The real-time dynamics of topological defects and turbulent configurations of gauge fields for electric and magnetic confinement are studied numerically within a 2+1D Abelian Higgs model. It is shown that confinement is appearing in such systems equilibrating after a strong initial quench such as the overpopulation of the infrared modes. While the final equilibrium state does not support confinement, metastable vortex defect configurations appearing in the gauge field are found to be closely related to the appearance of physically observable confined electric and magnetic charges. These phenomena are seen to be intimately related to the approach of a non-thermal fixed point of the far-from-equilibrium dynamical evolution, signaled by universal scaling in the gauge-invariant correlation function of the Higgs field. Even when the parameters of the Higgs action do not support condensate formation in the vacuum, during this approach, transient Higgs condensation is observed. We discuss implications of these results for the far-from-equilibrium dynamics of Yang–Mills fields and potential mechanisms of how confinement and condensation in non-Abelian gauge fields can be understood in terms of the dynamics of Higgs models. These suggest that there is an interesting new class of dynamics of strong coherent turbulent gauge fields with condensates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2011

Magnetic helicity transport in the advective gauge family

Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal magnetohydrodynamics takes the form of a purely advective flux. Numerical simulations of magnetohydrodynamic turbulence in this advective gauge family exhibit instabilities triggered by the build-up of unphysical irrotational contributions to the magnetic vector potential. As a remedy, the vector potential is evolved in a numerically well behaved gauge, from which the advective vector potential is obtained by a gauge transformation. In the kinematic regime, the magnetic helicity density evolves similarly to a passive scalar when resistivity is small and turbulent mixing is mild, i.e., when the fluid Reynolds number is not too large. In the dynamical regime, resistive contributions to the magnetic helicity flux in the advective gauge are found to be significant owing to the development of small length scales in the irrotational part of the magnetic vector potential.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2011

Geometrical gauge factor of directional electric potential drop sensors for creep monitoring

Directional electric potential drop measurements can be exploited for in-situ monitoring of creep in metals. The sensor monitors the variation in the ratio of the resistances measured simultaneously in the axial and lateral directions using a square-electrode configuration. This technique can efficiently separate the mostly isotropic common part of the resistivity variation caused by reversible temperature variations from the mostly anisotropic differential part caused by direct geometrical and indirect material effects of creep. Initially, this ratio is roughly proportional to the axial creep strain, while at later stages, the resistance ratio increases even faster with creep strain because of the formation of directional discontinuities such as preferentially oriented grain boundary cavities and multiple-site cracks in the material. Similarly to ordinary strain gauges, the relative sensitivity of the sensor is defined as a gauge factor that can be approximated as a sum of geometrical and material parts. This work investigated the geometrical gauge factor by analytical and experimental means. We found that under uniaxial stress square-electrode sensors exhibit geometrical gauge factors of about 4 and 5 in the elastic and plastic regimes, respectively, i.e., more than twice those of conventional strain gauges. Experimental results obtained on 304 stainless steel using a square-electrode electric potential drop creep sensor agree well with our theoretical predictions.

36 MATERIALS SCIENCE↗

DOE OSTI2012

A pressure gauge based on gas density measurement from analysis of the thermal noise of an atomic force microscope cantilever

We describe a gas-density gauge based on the analysis of the thermally-driven fluctuations of an atomic force microscope (AFM) cantilever. The fluctuations are modeled as a ring-down of a simple harmonic oscillator, which allows fitting of the resonance frequency and damping of the cantilever, which in turn yields the gas density. The pressure is obtained from the density using the known equation of state. In the range 10-220 kPa, the pressure readings from the cantilever gauge deviate by an average of only about 5% from pressure readings on a commercial gauge. The theoretical description we use to determine the pressure from the cantilever motion is based upon the continuum hypothesis, which sets a minimum pressure for our analysis. It is anticipated that the cantilever gauge could be extended to measure lower pressures given a molecular theoretical description. Alternatively, the gauge could be calibrated for use in the non-continuum range. Our measurement technique is similar to previous AFM cantilever measurements, but the analysis produces improved accuracy.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2014

Hydrogen atom excitation in intense attosecond laser field: Gauge dependence of dipole approximation

It is assumed that, the atomic excitations probability can be calculated using first order perturbation theory and dipole approximations. The validity of the dipole approximations had been examined by comparing the results with the results obtained by exact calculations within the first order perturbation theory[2]. Figure 1 shows the time dependence of the transition probability in the dipole approximation. From these plots it is obvious that, the probabilities obtained in the length gauge are higher than that in the velocity gauge, in the interaction period (−τ/2<t<τ/2). After passing this time interval, transition probabilities for these two gauges became equal to each other precisely. Moreover those results are equal to the corresponding exact (without the dipole approximation) calculations results. (Figure 2) Though the time evolution of the same transition probabilities are different for these cases, the final results are the same for all three cases, excluding the 6s-6p{sub 0} transition. For the later case, only the length gauge give a false results, but the velocity gauge give the same result as the exact one, for the final value of the transition probability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Redesigning rain gauges network in Johor using geostatistics and simulated annealing

Recently, many rainfall network design techniques have been developed, discussed and compared by many researchers. Present day hydrological studies require higher levels of accuracy from collected data. In numerous basins, the rain gauge stations are located without clear scientific understanding. In this study, an attempt is made to redesign rain gauge network for Johor, Malaysia in order to meet the required level of accuracy preset by rainfall data users. The existing network of 84 rain gauges in Johor is optimized and redesigned into a new locations by using rainfall, humidity, solar radiation, temperature and wind speed data collected during the monsoon season (November - February) of 1975 until 2008. This study used the combination of geostatistics method (variance-reduction method) and simulated annealing as the algorithm of optimization during the redesigned proses. The result shows that the new rain gauge location provides minimum value of estimated variance. This shows that the combination of geostatistics method (variance-reduction method) and simulated annealing is successful in the development of the new optimum rain gauge system.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Improving manganin gauge measurements near radiographic fiducials

In dynamic experiments diagnosed with radiography and stress gauges, the gauges are often placed adjacent to radio-graphic fiducials, such as Ta foil, which perturbs the stress measurement. We conducted experiments to test the performance of different arrangements of manganin stress gauges and Ta foils. Three different gauge/foil configurations were tested, as well as a solitary gauge as control. Gauge/foil layers were placed between high-density polyethylene (HDPE) discs and impacted by a projectile in a gas gun, a simplification of a dynamic, high explosive experiment configuration. The stress measurements were minimally perturbed when a section of foil was removed near the active element of the gauge, as expected. In conclusion, a follow-up experiment showed that the modification to the foil has minimal impact on the radiographic measurement of the dynamic flow.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2011

Gauged M-flation, its UV sensitivity and spectator species

In this paper we study gauged M-flation, an inflationary model in which inflation is driven by three N × N scalar field matrices in the adjoint representation of U(N) gauge group. We focus our study on the gauged M-flation model which could be derived from the dynamics of a stack of D3-branes in appropriate background flux. The background inflationary dynamics is unaltered compared to the ungauged case of \cite(Ashoorioon:2009wa), while the spectrum of ''spectator species'', the isocurvature modes, differs from the ungauged case. Presence of a large number of spectators, although irrelevant to the slow-roll inflationary dynamics, has been argued to lower the effective UV cutoff Λ of the theory from the Planck mass M{sub pl}, putting into question the main advantage of M-flation in not having super-Planckian field values and unnaturally small couplings. Through a careful analysis of the spectrum of the spectators we argue that, contrary to what happens in N-flation models, M-flation is still UV safe with the modified (reduced) effective UV cutoff Λ, which we show to be of order (0.5−1) × 10{sup −1}M{sub pl}. Moreover, we argue that the string scale in our gauged M-flation model is larger than Λ by a factor of 10 and hence one can also neglect stringy effects. We also comment on the stability of classical inflationary paths in the gauged M-flation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Gauge-flation confronted with Planck

Gauge-flation is a recently proposed model in which inflation is driven solely by a non-Abelian gauge field thanks to a specific higher order derivative operator. The nature of the operator is such that it does not introduce ghosts. We compute the cosmological scalar and tensor perturbations for this model, improving over an existing computation. We then confront these results with the Planck data. The model is characterized by the quantity γ ≡ g{sup 2}Q{sup 2}/H{sup 2} (where g is the gauge coupling constant, Q the vector vev, and H the Hubble rate). For γ < 2, the scalar perturbations show a strong tachyonic instability. In the stable region, the scalar power spectrum n{sub s} is too low at small γ, while the tensor-to-scalar ratio r is too high at large γ. No value of γ leads to acceptable values for n{sub s} and r, and so the model is ruled out by the CMB data. The same behavior with γ was obtained in Chromo-natural inflation, a model in which inflation is driven by a pseudo-scalar coupled to a non-Abelian gauge field. When the pseudo-scalar can be integrated out, one recovers the model of Gauge-flation plus corrections. It was shown that this identification is very accurate at the background level, but differences emerged in the literature concerning the perturbations of the two models. On the contrary, our results show that the analogy between the two models continues to be accurate also at the perturbative level.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Stability analysis of inflation with an SU(2) gauge field

We study anisotropic cosmologies of a scalar field interacting with an SU(2) gauge field via a gauge-kinetic coupling. We analyze Bianchi class A models, which include Bianchi type I, II, VI{sub 0}, VII{sub 0}, VIII and IX. The linear stability of isotropic inflationary solution with background magnetic field is shown, which generalizes the known results for U(1) gauge fields. We also study anisotropic inflationary solutions, all of which turn out to be unstable. Then nonlinear stability for the isotropic inflationary solution is examined by numerically investigating the dependence of the late-time behaviour on the initial conditions. We present a number of novel features that may well affect physical predictions and viability of the models. First, in the absence of spatial curvature, strong initial anisotropy leads to a rapid oscillation of gauge field, thwarting convergence to the inflationary attractor. Secondly, the inclusion of spatial curvature destabilizes the oscillatory attractor and the global stability of the isotropic inflation with gauge field is restored. Finally, based on the numerical evidence combined with the knowledge of the eigenvalues for various inflationary solutions, we give a generic lower-bound for the duration of transient anisotropic inflation, which is inversely proportional to the slow-roll parameter.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Primordial anisotropies in gauged hybrid inflation

We study primordial anisotropies generated in the model of gauged hybrid inflation in which the complex waterfall field is charged under a U(1)gauge field. Primordial anisotropies are generated either actively during inflation or from inhomogeneities modulating the surface of end of inflation during waterfall transition. We present a consistent δN mechanism to calculate the anisotropic power spectrum and bispectrum. We show that the primordial anisotropies generated at the surface of end of inflation do not depend on the number of e-folds and therefore do not produce dangerously large anisotropies associated with the IR modes. Furthermore, one can find the parameter space that the anisotropies generated from the surface of end of inflation cancel the anisotropies generated during inflation, therefore relaxing the constrains on model parameters imposed from IR anisotropies. We also show that the gauge field fluctuations induce a red-tilted power spectrum so the averaged power spectrum from the gauge field can change the total power spectrum from blue to red. Therefore, hybrid inflation, once gauged under a U(1) field, can be consistent with the cosmological observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Gravitational wave probes of massive gauge bosons at the cosmological collider

We extend the reach of the "cosmological collider" for massive gauge boson production during inflation from the CMB scales to the interferometer scales. Considering a Chern-Simons coupling between the gauge bosons and the pseudoscalar inflaton, one of the transverse gauge modes is efficiently produced and its inverse decay leaves an imprint in the primordial scalar and tensor perturbations. We study the correlation functions of these perturbations and derive the updated constraints on the parameter space from CMB observables. We then extrapolate the tensor power spectrum to smaller scales consistently taking into account the impact of the gauge field on inflationary dynamics. Our results show that the presence of massive gauge fields during inflation can be detected from characteristic gravitational wave signals encompassing the whole range of current and planned interferometers.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis

Maintaining local interactions in the quantum simulation of gauge field theories relegates most states in the Hilbert space to be unphysical—theoretically benign, but experimentally difficult to avoid. Reformulations of the gauge fields can modify the ratio of physical to gauge-variant states often through classically preprocessing the Hilbert space and modifying the representation of the field on qubit degrees of freedom. This paper considers the implications of representing SU(3) Yang-Mills gauge theory on a lattice of irreducible representations in both a global basis of projected global quantum numbers and a local basis in which controlled-plaquette operators support efficient time evolution. Classically integrating over the internal gauge space at each vertex (e.g., color isospin and color hypercharge) significantly reduces both the qubit requirements and the dimensionality of the unphysical Hilbert space. Initiating tuning procedures that may inform future calculations at scale, the time evolution of one and two plaquettes are implemented on one of IBM’s superconducting quantum devices, and early benchmark quantities are identified. The potential advantages of qudit environments, with either constrained two-dimensional hexagonal or one dimensional nearest-neighbor internal state connectivity, are discussed for future large-scale calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗