Gauge Field Research Articles

Note on higher-group structure in 6d self-dual gauge theory

We analyze higher-group structure of a 6d model coupled with a self-dual 2-form gauge field. This model is defined from 6d axion-electrodynamics with a 1-form Chern-Weil(CW) symmetry gauged dynamically. The gauging leads to a Green-Schwarz-West-Sagnotti(GSWS) term, which gives rise to an anomaly through a GSWS transformation acting on the 2-form gauge field. We cancel this anomaly by gauging a 3-form CW symmetry in 6d axion-electrodynamics. We find out the global symmetries in the resultant model and derive the gauge invariant action in the presence of the background gauge fields. It is argued that a discrete 1-form symmetry is anomalous because turning on the associated background gauge field causes quantum inconsistency due to an operator-valued ambiguity. Higher-group structure in this model that is manifested as a Green-Schwarz-like transformation for CW background gauge fields is discussed.

Nonminimal coupling holographic superconductors

We explore a holographic superconductor model in which a real scalar field is nonminimally coupled to a gauge field. We consider several types of the nonminimal coupling function h(ψ) including exponential, hyperbolic (cosh), power-law, and fractional forms. We investigate the influences of the nonminimal coupling parameter α on condensation, critical temperature, and conductivity. We can categorize our results in two groups. In the first group, conductor/superconductor phase transition is easier to occur for larger values of α, while in the second group stronger effects of the nonminimal coupling makes the formation of scalar hair harder. Although the real and imaginary parts of conductivity are impressed by different forms of h(ψ), they follow some universal behaviors such as connecting with each other through Kramers–Kronig relation in ω → 0 limit or the appearance of gap frequency at low temperatures around ωg ∼ 8 Tc, which shifts to larger values by increasing the strength of α. Among all forms of h(ψ) we observe that h(ψ) = 1 + αψ2 gives us better information in wide range of nonminimal coupling constant and temperature. Choosing the best form of h(ψ), we construct a family of solutions for holographic conductor/superconductor phase transitions to discover the effect of the hyperscaling violation when the gauge and scalar fields are nonminimally coupled. we find that the critical temperature increases for higher effects of hyperscaling violation θ and nonminimal coupling constant α. By increasing these two parameters, we obtain lower values of condensation which means that conductor/superconductor phase transition will acquire easier. Furthermore, we understand that the hyperscaling violation affects the conductivity σ of the holographic superconductors and changes the expected relation in the gap frequency. Some universal behaviors like infinite DC conductivity are observed. In addition, we consider a five-dimensional Gauss–Bonnet (GB) black hole with a flat horizon. We find out that the critical temperature decreases for larger values of GB coupling constant, λ, or smaller values of nonminimal coupling constant, α, which means that the condensation is harder to form. Moreover, we study the electrical conductivity in the holographic setup. We observe that the gap frequency shifts to larger values for stronger λ, and becomes flat by increasing α.

Semi-transparent boundary in Lee–Wick electrodynamics

In this paper, we investigate certain aspects of Lee–Wick electrodynamics near a semitransparent planar mirror. Specifically, we derive the modified propagator for the Lee–Wick gauge field in the presence of the mirror and conduct a detailed analysis of the interaction energy and the interaction force that arise between the mirror and a stationary point-like charge. We demonstrate that there are several peculiarities in this interaction compared to the results obtained for Maxwell electrodynamics. Our focus is on the divergences mitigated by the Podolsky mass term.

Light fermion masses in partially deconstructed models

Considering a theory space consisting of a large number of five-dimensional Dirac fermion field theories including background abelian gauge fields, we can construct a theory similar to a continuous six-dimensional theory compactified with two-dimensional manifolds with and without magnetic flux or orbifolds as extra dimensions. This method, called dimensional deconstruction, can be used to construct a model with one-dimensional discrete space, which represents general graph structures. In this paper, we propose the models with two extra dimensions, which resemble two-dimensional tori, cylinders, and rectangular regions, as continuum limits. We also try to build a model that mimics one with the two-dimensional orbifold compactification.

Fractional spins, unfolding, and holography. Part II. 4D higher spin gravity and 3D conformal dual

This paper completes the analysis initiated in the companion work arXiv:2403.02283 — referred to as Paper I — by showing how Vasiliev’s 4D higher-spin gravity (HSG) and 3D coloured conformal matter fields coupled to conformal higher-spin gauge fields and colour gauge fields (coloured conformal HSG, or CCHSG) emerge as consistent reductions of a common parent model. The latter is a Frobenius-Chern-Simons model with superconnection valued in a fractional-spin extension of Vasiliev’s higher-spin algebra, and was defined and studied in Paper I. Here, we i) realize HSG as a subcase of a more general 4D reduction, describing HSG coupled to coloured, fractional-spin matter, which we refer to as 4D fractional-spin gravity; ii) study the CCHSG model, in particular exhibiting the crucial role played by novel colour gauge fields in coupling conformal matter to conformal HSG, thereby completing the models due to Vasiliev and Nilsson; iii) extract conformal currents and composite coloured sources in an expansion of the CCHSG model around 3D Minkowskian leaves; and iv) compare our results with Vasiliev’s holography proposal of arXiv:1203.5554. The common origin of HSG and CCHSG, besides relating the two models directly, is the starting point for establishing the holographic correspondence between the two models via overlap conditions, to be presented separately.

Topological 4D gravity and gravitational defects

Abstract Using the Chern-Simons formulation of AdS3 gravity as well as the Costello-
Witten-Yamazaki (CWY) theory for quantum integrability, we construct a novel
topological 4D gravity given by Eq(5.1) with observables based on gravitational
gauge field holonomies. The field action Sgrav 4D of this gravity has a gauge symmetry SL(2,C) and reads also as the difference SCWYL 4D - SCWYR 4D with 4D Chern-Simons field actions SCWYL/R 4D given by left/right CWY theory Eq(3.9). We also use this 4D gravity derivation to build observables describing gravitational topological defects and their interactions. We conclude our study with few comments regarding quantum integrability and the extension of AdS3/CFT2 correspondence with regard to the obtained topological 4D gravity.

Renormalization flow of nonlinear electrodynamics

We study the renormalization flow of generic actions that depend on the invariants of the field strength tensor of an Abelian gauge field. While the Maxwell action defines a Gaussian fixed point, we search for further non-Gaussian fixed points or rather fixed functions, i.e., globally existing Lagrangians of the invariants. Using standard small-field expansion techniques for the resulting functional flow equation, a large number of fixed points is obtained, which—in analogy to recent findings for a shift-symmetric scalar field—we consider as approximation artifacts. For the construction of a globally existing fixed function, we pay attention to the use of proper initial conditions. Parametrizing the latter by the photon anomalous dimension, both the coefficients of the weak-field expansion are fully determined and those of the large-field expansion can be matched such that a global fixed function can be constructed for magnetic fields. The anomalous dimension also governs the strong-field limit. Our results provide evidence for the existence of a continuum of non-Gaussian fixed points parametrized by a small positive anomalous dimension below a critical value. We discuss the implications of this result within various scenarios with and without additional matter. For the strong-field limit of the 1PI QED effective action, where the anomalous dimension is determined by electronic fluctuations, our result suggests the existence of a singularity free strong-field limit, circumventing the standard conclusions connected to the perturbative Landau pole. Published by the American Physical Society 2024

A holographic model of magnetohydrodynamics with fortuitous SO(3) symmetry

We study magnetohydrodynamics using holography. The gravity model is closely related to the STU supergravity in five dimensions and admits an analytical black brane solution carrying the conserved charge dual to the magnetic 1-form symmetry of the magnetohydrodynamic system. The black brane solution features a fortuitous SO(3) symmetry, providing a new symmetry principle for describing the magnetohydrodynamics. Since the bulk theory contains multiple 2-form gauge fields, the resistivity becomes matrix-valued. We find that the antisymmetric part of the resistivity matrix exhibits novel features depending on the UV cut-off of the theory. We also compute the shear and bulk viscosities and find that the bulk viscosity is proportional to the shear viscosity. Remarkably, the proportionality constant is exactly what is required for conformality, despite the zeroth-order energy-momentum tensor not being trace-free.

From the Cosserats mechanics backgrounds to modern field theory

In the paper, yet weekly known, Cosserats’ original four concepts as follow: the four-time unification of rigid body dynamics, statics of flexible rods, statics of elastic surfaces and 3D deformable body dynamics; the intrinsic formulation based on the local, von Helmholtz symmetry group of monodromy; the invariance under the Euclidean group. The concept of a set of low-dimensional branes immersed into Euclidean space are revalorized and explained in terms of the modern gauge field theory and the extended strings theory. Additionally, some useful mathematical tools that connect the continuum mechanics and the classical field theory (for instance, the convective coordinates, von Mises’ “Motorrechnung”, the Grassmann extensions, Euclidean invariance, etc.) are involved in the historical explanation that how the ideas were developing themself.

Correlated scalar perturbations and gravitational waves from axion inflation

Abstract The scalar and tensor fluctuations generated during inflation can be correlated, if arising from the same underlying mechanism. In this paper we investigate such correlation in the model of axion inflation, where the rolling inflaton produces quanta of a U(1) gauge field which, in turn, source scalar and tensor fluctuations. We compute the primordial correlator of the curvature perturbation, ζ, with the gravitational energy density, Ω GW , at frequencies probed by gravitational wave detectors. This two-point function receives two contributions: one arising from the correlation of gravitational waves with the scalar perturbations generated by the standard mechanism of amplification of vacuum fluctuations, and the other coming from the correlation of gravitational waves with the scalar perturbations sourced by the gauge field. Our analysis shows that the former effect is generally dominant. For typical values of the parameters, the correlator, normalized by the amplitude of ζ and by the fractional energy in gravitational waves at interferometer frequencies, turns out to be of the order of 10-4 ÷ 10-2.

Linearized second law for higher curvature gravity and nonminimally coupled vector fields

Expanding the work of Wall [], we show that black holes obey a second law for linear perturbations to bifurcate Killing horizons, in any covariant higher curvature gravity coupled to scalar and vector fields. The vector fields do not need to be gauged, and (like the scalars) can have arbitrary nonminimal couplings to the metric. The increasing entropy has a natural expression in covariant phase space language, which makes it manifestly invariant under Jacobson-Kang-Myers ambiguities. An explicit entropy formula is given for f(Riemann) gravity coupled to vectors, where at most one derivative acts on each vector. Besides the previously known curvature terms, there are three extra terms involving differentiating the Lagrangian by the symmetric vector derivative (which therefore vanish for gauge fields). Published by the American Physical Society 2024

Nonperturbative four-gluon vertex in soft kinematics

We present a nonperturbative study of the form factor associated with the projection of the full four-gluon vertex on its classical tensor, for a set of kinematics with one vanishing and three arbitrary external momenta. The treatment is based on the Schwinger-Dyson equation governing this vertex, and a large-volume lattice simulation, involving ten thousand gauge field configurations. The key hypothesis employed in both approaches is the “planar degeneracy”, which classifies diverse configurations by means of a single variable, thus enabling their meaningful “averaging”. The results of both approaches show notable agreement, revealing a considerable suppression of the averaged form factor in the infrared. The deviations from the exact planar degeneracy are discussed in detail, and a supplementary variable is used to achieve a more accurate description. The effective charge defined through this special form factor is computed within both approaches, and the results obtained are in excellent agreement.

Second resonance of the Higgs field: motivations, experimental signals, unitarity constraints

Perturbative calculations predict that the effective potential of the Standard Model should have a new minimum, well beyond the Planck scale, which is much deeper than the electroweak vacuum. So far, most authors have accepted the metastability scenario in a cosmological perspective which is needed to explain why the theory remains trapped in our electroweak vacuum but requires to control the properties of matter in the extreme conditions of the early universe. As an alternative, one can consider the completely different idea of a non-perturbative effective potential that, as at the beginning of the Standard Model, is restricted to the pure Φ4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi ^4$$\\end{document} sector but is consistent with the indications of the now existing analytical and numerical studies, namely “triviality” and a description of SSB as weak first-order phase transition. In this approach, the electroweak vacuum is now the lowest energy state because, besides the state with mass mh=125\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_h=125$$\\end{document} GeV, defined by the quadratic shape of the potential at its minimum, there is a second much larger mass scale (MH)Theor∼690(30)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(M_H)^\ extrm{Theor} \\sim 690(30)$$\\end{document} GeV associated with the zero-point energy determining the potential depth. Despite its large mass, the heavier state would couple to longitudinal Ws with the same typical strength as the low-mass state at 125 GeV and thus represent a relatively narrow resonance mainly produced at LHC by gluon-gluon fusion. Therefore, it is interesting that, in the LHC data, one can find combined indications of a new resonance of mass (MH)comb∼685(10)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(M_H)^\ extrm{comb} \\sim 685 (10)$$\\end{document} GeV, with a statistical significance which is far from negligible. Since this non-negligible evidence could become an important new discovery with forthcoming data, we outline further refinements of the theoretical predictions, that could be obtained by implementing unitarity constraints, in the presence of fermion and gauge fields, with the type of coupled-channel calculations nowadays used in meson spectroscopy.

Examples of Zero Modes of the Faddeev–Popov Operator for the SU(2) Gauge Field

Examples of Zero Modes of the Faddeev–Popov Operator for the SU(2) Gauge Field

Non-Abelian chiral dynamics in a lattice under synthetic SU(2) gauge fields

Non-Abelian chiral dynamics in a lattice under synthetic SU(2) gauge fields

Chiral dynamics of ultracold atoms under a tunable SU(2) synthetic gauge field

Chiral dynamics of ultracold atoms under a tunable SU(2) synthetic gauge field

O(9, 25) symmetry of heterotic string theory at orders α′, α′2

In a recent study, we have observed that by imposing a truncated T-duality transformation on the circular reduction of the bosonic couplings in the heterotic theory at four- and six-derivative orders, we can calculate these couplings in a particular YM gauge where the YM potential vanishes but its field strength remains non-zero. Importantly, the coupling constants are independent of the gauge choice, so these results are valid across different YM gauge choices.In this work, we explore the cosmological reduction of these couplings when the YM gauge fields belong to the Cartan subalgebra of SO(32) or E8 × E8. We demonstrate that after applying appropriate one-dimensional field redefinitions and total derivative terms, the couplings can be expressed in a proposed O(9, 25)-invariant canonical form, which is the extension of the canonical O(9, 9)-invariant form for just the NS-NS fields proposed by Hohm and Zwiebach. This O(9, 25)-invariant expression is in terms of the trace of the first time derivative of the generalized metric, which encompasses both the YM field and the NS-NS fields.

Fractional spins, unfolding, and holography. Part I. Parent field equations for dual higher-spin gravity reductions

In this work and in the companion paper arXiv:2403.02301, we initiate an approach to holography based on the AKSZ formalism. As the first step, we refine Vasiliev’s holography proposal in arXiv:1203.5554 by obtaining 4D higher-spin gravity (HSG) and 3D coloured conformal higher-spin gravity (CCHSG) — i.e., coloured conformal matter fields coupled to conformal higher-spin gauge fields and colour gauge fields — as two distinct and classically consistent reductions of a single parent theory. The latter consists, on-shell, of a flat superconnection valued in a fractional-spin extension of Vasiliev’s higher-spin algebra. The HSG and CCHSG reductions are characterized by dual structure groups and two-form cohomology elements, and their embedding in a common parent model provides a rationale for deriving holographic relations from multi-dimensional AKSZ partition functions on cylinders with dual boundary conditions, to appear separately. In this work we i) construct the underlying non-commutative geometry as a metaplectic operator algebra represented in a Hermitian module of a pair of conformal particles; ii) identify a discrete modular group, arising from twisted boundary conditions of the first-quantized system, and connecting different boundary conditions of the second-quantized system; and iii) identify the holonomies, structure groups and two-form cohomology elements that characterize the HSG and CCHSG reductions, and equate the dual second Chern classes.

Do neutrinos bend? Consequences of an ultralight gauge field as dark matter

An ultralight gauge boson could address the missing cosmic dark matter, with its transverse modes contributing to a relevant component of the galactic halo today. We show that, in the presence of a coupling between the gauge boson and neutrinos, these transverse modes affect the propagation of neutrinos in the galactic core. Neutrinos emitted from galactic or extra-galactic supernovae could be delayed by δt=10−8–101s for the gauge boson masses mA′=10−23–10−19eV and the coupling with the neutrino g=10−27–10−20. While we do not focus on a specific formation mechanism for the gauge boson as the dark matter in the early Universe, we comment on some possible realizations. We discuss model-dependent current bounds on the gauge coupling from fifth-force experiments, as well as future explorations involving supernovae neutrinos. We consider the concrete case of the DUNE facility, where the coupling can be tested down to g≃10−27 for neutrinos coming from a supernova event at a distance d=10kpc from Earth.

Numerical indication that center vortices drive dynamical mass generation in QCD

The first calculation of the response of the momentum space quark propagator to center vortices in the ground state fields of QCD is presented. Center vortices are identified on 2+1-flavor dynamical gauge fields with mπ≃156 MeV to obtain the vortex-removed and vortex-only quark propagator. Dynamical mass generation is found to vanish upon vortex removal, while the vortex-only field is able to generate dynamical mass. These new signatures strengthen the lattice QCD evidence indicating that center vortices underpin both dynamical chiral symmetry breaking and quark confinement. Published by the American Physical Society 2024