Gauge Field Action Research Articles

HIDING AND CONFINING CHARGES VIA "TUBE-LIKE" WORMHOLES

We describe two interesting effects in wormhole physics. First, we find that a genuinely charged matter source of gravity and electromagnetism may appear electrically neutral to an external observer — a phenomenon opposite to the famous Misner–Wheeler "charge without charge" effect. We show that this phenomenon takes place when coupling a bulk gravity/nonlinear-gauge-field system self-consistently to a codimension-one charged lightlike brane as a matter source. The "charge-hiding" effect occurs in a self-consistent wormhole solution of the above coupled gravity/nonlinear-gauge-field/lightlike-brane system which connects a noncompact "universe," comprising the exterior region of Schwarzschild–(anti-)de Sitter (or purely Schwarzschild) black hole beyond the internal (Schwarzschild) horizon, to a Levi-Civita–Bertotti–Robinson-type ("tube-like") "universe" with two compactified dimensions via a wormhole "throat" occupied by the charged lightlike brane. In this solution the whole electric flux produced by the charged lightlike brane is expelled into the compactified Levi-Civita–Bertotti–Robinson-type "universe" and, consequently, the brane is detected as neutral by an observer in the Schwarzschild–(anti-)de Sitter "universe." Next, the above "charge-hiding" solution can be further generalized to a truly charge-confining wormhole solution when we couple the bulk gravity/nonlinear-gauge-field system self-consistently to two separate codimension-one charged lightlike branes with equal in magnitude but opposite charges. The latter system possesses a "two-throat" wormhole solution, where the "left-most" and the "right-most" "universes" are two identical copies of the exterior region of the neutral Schwarzschild–de Sitter black hole beyond the Schwarzschild horizon, whereas the "middle" "universe" is of generalized Levi-Civita–Bertotti–Robinson "tube-like" form with geometry dS2 ×S2 (dS2 being the two-dimensional de Sitter space). It comprises the finite-extent intermediate region of dS2 between its two horizons. Both "throats" are occupied by the two oppositely charged lightlike branes and the whole electric flux produced by the latter is confined entirely within the middle finite-extent "tube-like" "universe." A crucial ingredient is the special form of the nonlinear gauge field action, which contains both the standard Maxwell term as well as a square root of the latter. This theory was previously shown to produce a QCD-like confining dynamics in flat space–time.

ADVANCES IN TERNARY AND OCTONIONIC GAUGE FIELD THEORIES

A ternary gauge field theory is explicitly constructed based on a totally antisymmetric ternary-bracket structure associated with a 3-Lie algebra. It is shown that the ternary infinitesimal gauge transformations do obey the key closure relations [δ1, δ2] = δ3. Invariant actions for the 3-Lie algebra-valued gauge fields and scalar fields are displayed. We analyze and point out the difficulties in formulating a nonassociative octonionic ternary gauge field theory based on a ternary-bracket associated with the octonion algebra and defined earlier by Yamazaki. It is shown that a Yang–Mills-like quadratic action is invariant under global (rigid) transformations involving the Yamazaki ternary octonionic bracket, and that there is closure of these global (rigid) transformations based on constant antisymmetric parameters Λab = - Λba. Promoting the latter parameters to space–time dependent ones Λab(xμ) allows one to build an octonionic ternary gauge field theory when one imposes gauge covariant constraints on the latter gauge parameters leading to field-dependent gauge parameters and nonlinear gauge transformations. In this fashion one does not spoil the gauge invariance of the quadratic action under this restricted set of gauge transformations and which are tantamount to space–time dependent scalings (homothecy) of the gauge fields.

Generalized cosmological term from Maxwell symmetries

By gauging the Maxwell spacetime algebra the standard geometric framework of Einstein gravity with cosmological constant term is extended by adding six fourvector fields A_\mu^{ab}(x) associated with the six abelian tensorial charges in the Maxwell algebra. In the simplest Maxwell extension of Einstein gravity this leads to a generalized cosmological term that includes a contribution from these vector fields. We also consider going beyond the basic gravitational model by means of bilinear actions for the new Abelian gauge fields. Finally, an analogy with the supersymmetric generalization of gravity is indicated. In an Appendix, we propose an equivalent description of the model in terms of a shift of the standard spin connection by the A_\mu^{ab}(x) fields.

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.

Elastic Properties of Vanadium Pentoxide Aggregates and Topological Defects

We study the aqueous solution of vanadium pentoxide by using topology methods. The experiments by Zocher, Kaznacheev, and Dogic exhibited that in the sol phases of V2O5–H2O, the tactoid droplets of V2O5 can coalesce. In the magnetic field, this effect is associated with a gauge field action, viz. we consider coalescence (“junction,” in the topologically more convenient term) of droplets as annihilation of topological defects, concerning with the tactoid geometry. We have shown, that in the magnetic field, the tactoid junction is mainly caused by non-Abelian monopoles (vortons), whereas the Abelian defects almost do not annihilate. Taking into account this annihilation mechanism, the estimations of time-aging of the V2O5–H2O sols may be specified.

Hadron spectrum, quark masses, and decay constants from light overlap fermions on large lattices

We present results from a simulation of quenched overlap fermions with Luescher-Weisz gauge field action on lattices up to 24{sup 3}48 and for pion masses down to {approx_equal}250 MeV. Among the quantities we study are the pion, rho, and nucleon masses; the light and strange quark masses; and the pion decay constant. The renormalization of the scalar and axial vector currents is done nonperturbatively in the RI-MOM scheme. The simulations are performed at two different lattice spacings, a{approx_equal}0.1 fm and {approx_equal}0.15 fm, and on two different physical volumes, to test the scaling properties of our action and to study finite volume effects. We compare our results with the predictions of chiral perturbation theory and compute several of its low-energy constants. The pion mass is computed in sectors of fixed topology as well.

Tensor Gauge Fields in Arbitrary Representations of GL(D, $${\mathbb{R})}$$ : II. Quadratic Actions

Quadratic, second-order, non-local actions for tensor gauge fields transforming in arbitrary irreducible representations of the general linear group in D-dimensional Minkowski space are explicitly written in a compact form by making use of Levi–Civita tensors. The field equations derived from these actions ensure the propagation of the correct massless physical degrees of freedom and are shown to be equivalent to non-Lagrangian local field equations proposed previously. Moreover, these actions allow a frame-like reformulation a la MacDowell–Mansouri, without any trace constraint in the tangent indices.

Noncommutative QFT and Renormalization

Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to ϕ3 models and use the heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a θ-deformed space and derive noncommutative gauge field actions.

Perturbative Wilson loops from unquenched Monte Carlo simulations at weak couplings

Perturbative expansions of several small Wilson loops are computed through next-to-next-to-leading order in unquenched lattice QCD, from Monte Carlo simulations at weak couplings. This approach provides a much simpler alternative to conventional diagrammatic perturbation theory, and is applied here for the first time to full QCD. Two different sets of lattice actions are considered: one set uses the unimproved plaquette gluon action together with the unimproved staggered-quark action; the other set uses the one-loop-improved Symanzik gauge-field action together with the so-called ``asqtad'' improved-staggered quark action. Simulations are also done with different numbers of dynamical fermions. An extensive study of the systematic uncertainties is presented, which demonstrates that the small third-order perturbative component of the observables can be reliably extracted from simulation data. We also investigate the use of the rational hybrid Monte Carlo algorithm for unquenched simulations with unimproved-staggered fermions. Our results are in excellent agreement with diagrammatic perturbation theory, and provide an important cross-check of the perturbation theory input to a recent determination of the strong coupling $\alpha_{\bar{\rm MS}}(M_Z)$ by the HPQCD collaboration.

Sum rules for the Dirac spectrum of the Schwinger model

The inverse eigenvalues of the Dirac operator in the Schwinger model satisfy the same Leutwyler-Smilga sum rules as in the case of QCD with one flavor. In this paper we give a microscopic derivation of these sum rules in the sector of arbitrary topological charge. We show that the sum rules can be obtained from the clustering property of the scalar correlation functions. This argument also holds for other theories with a mass gap and broken chiral symmetry such as QCD with one flavor. For QCD with several flavors a modified clustering property is derived from the low energy chiral Lagrangian. We also obtain sum rules for a fixed external gauge field and show their relation with the bosonized version of the Schwinger model. In the sector of topological charge $\nu$ the sum rules are consistent with a shift of the Dirac spectrum away from zero by $\nu/2$ average level spacings. This shift is also required to obtain a nonzero chiral condensate in the massless limit. Finally, we discuss the Dirac spectrum for a closely related two-dimensional theory for which the gauge field action is quadratic in the the gauge fields. This theory of so called random Dirac fermions has been discussed extensively in the context of the quantum Hall effect and d-wave super-conductors.

The quantum one loop trace anomaly of the higher spin conformal conserved currents in the bulk of [formula omitted

An analysis of the structure and singularities of the one loop two point function of the higher spin traceless and conserved currents constructed from the single scalar field in AdS space is presented. The detailed renormalization procedure is constructed and the quantum violation of the traceless Ward identity is investigated. The connection with the one loop effective action for higher spin gauge fields is discussed.

Hierarchy of massive gauge fields

An explicitly gauge invariant polynomial action for massive gauge fields is proposed. For different values of parameters it describes massive Yang–Mills field, the Higgs–Kibble model, the model with spontaneously broken symmetry and two scalar mesons.

Systematics of staggered fermion spectral properties and topology

The spectral properties of a variety of improved staggered operators are studied in quenched QCD. The systematic dependence of the infrared eigenvalue spectrum on i) improvement in the staggered operator, ii) improvement in the gauge field action, iii) lattice spacing and iv) lattice volume, is analyzed. It is observed that eigenmodes with small eigenvalues and large chirality appear as the level of improvement increases or as one approaches the continuum limit. These eigenmodes can be identified as the ``zero modes'' which contribute to the chirality associated, via the index theorem, with the topology of the background gauge field. This gives evidence that staggered fermions are sensitive to gauge field topology. After successfully identifying these would-be chiral zero modes, the distribution of the remaining non-chiral modes is compared with the predictions of Random Matrix Theory in different topological sectors. Satisfactory agreement is obtained.

Analytic smearing ofSU(3)link variables in lattice QCD

An analytic method of smearing link variables in lattice QCD is proposed and tested. The differentiability of the smearing scheme with respect to the link variables permits the use of modern Monte Carlo updating methods based on molecular dynamics evolution for gauge-field actions constructed using such smeared links. In examining the smeared mean plaquette and the static quark-antiquark potential, no degradation in effectiveness is observed as compared to link smearing methods currently in use, although an increased sensitivity to the smearing parameter is found.

Quark spectra and light hadron phenomenology from overlap fermions with improved gauge field action

We present first results from a simulation of quenched overlap fermions with improved gauge field action. Among the quantities we study are the spectral properties of the overlap operator, the chiral condensate and topological charge, quark and hadron masses, and selected nucleon matrix elements. To make contact with continuum physics, we compute the renormalization constants of quark bilinear operators in perturbation theory and beyond.

Effective action for brane localized gauge fields

The low energy effective action including gauge field degrees of freedom on a non-BPS p=2 brane embedded in a N=1, D=4 target superspace is obtained through the method of nonlinear realizations of the associated super-Poincare symmetries. The invariant interactions of the gauge fields and the brane excitation modes corresponding to the Nambu-Goldstone degrees of freedom resulting from the broken space translational symmetry and the target space supersymmetries are determined. Brane localized matter field interactions with the gauge fields are obtained through the construction of the combined gauge and super-Poincare covariant derivatives for the matter fields.

Comparison of | Q|=1 and | Q|=2 gauge-field configurations on the lattice four-torus

It is known that exactly self-dual gauge-field configurations with topological charge | Q|=1 cannot exist on the untwisted continuum four-torus. We explore the manifestation of this remarkable fact on the lattice four-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et al. for SU(2). We identify three distinct signals for the instability of | Q|=1 configurations, and show that these signals manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for the individual instantons which make up our | Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than the local discretization effects which cause the eventual disappearance of the would-be single instanton. Monte-Carlo generated SU(3) gauge-field configurations are cooled to the self-dual limit using an O(a 4) -improved gauge action chosen to have small but positive O(a 6) errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the O(a 4) -improved gauge-field action with an O(a 4) -improved action constructed from the square of an O(a 4) -improved lattice field-strength tensor, thus having different O(a 6) discretization errors. The number of action-density peaks, the instanton size, and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of | Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.

Remarks on the interaction between Born–Infeld solitons

We consider the abelian Higgs model as well as the SU(2) Georgi–Glashow model in which the gauge field action is replaced by a nonlinear Born–Infeld (BI) action. We study soliton solutions arising in these models, namely the vortex and monopole solutions, respectively. We construct formulae which provide good approximations for the mass of the BI deformed solitons using only the data of the undeformed solutions. The results obtained indicate that in the self-dual limit, the BI interaction leads to bound vortices, while for monopoles it gives rise to repulsion.

Improved smoothing algorithms for lattice gauge theory

The relative smoothing rates of various gauge field smoothing algorithms are investigated on ${\cal O}(a^2)$-improved $\suthree$ Yang--Mills gauge field configurations. In particular, an ${\cal O}(a^2)$-improved version of APE smearing is motivated by considerations of smeared link projection and cooling. The extent to which the established benefits of improved cooling carry over to improved smearing is critically examined. We consider representative gauge field configurations generated with an ${\cal O}(a^2)$-improved gauge field action on $\1$ lattices at $\beta=4.38$ and $\2$ lattices at $\beta=5.00$ having lattice spacings of 0.165(2) fm and 0.077(1) fm respectively. While the merits of improved algorithms are clearly displayed for the coarse lattice spacing, the fine lattice results put the various algorithms on a more equal footing and allow a quantitative calibration of the smoothing rates for the various algorithms. We find the relative rate of variation in the action may be succinctly described in terms of simple calibration formulae which accurately describe the relative smoothness of the gauge field configurations at a microscopic level.

Finite baryon density effects on gauge field dynamics

We discuss the effective action for QCD gauge fields at finite temperatures and densities, obtained after integrating out the hardest momentum scales from the system. We show that a non-vanishing baryon density induces a charge conjugation (C) odd operator to the gauge field action, proportional to the chemical potential. Even though it is parametrically smaller than the leading C even operator, it could have an important effect on C odd observables. The same operator appears to be produced by classical kinetic theory, allowing in principle for a non-perturbative study of such processes.