arXiv subjects

Jackson A. Mickley

Publications and source records attributed to Jackson A. Mickley.

9 recordsLinked to original sources

arXiv2026

Understanding the structure of nucleon excitations from their wavefunctions

Relativistic wavefunctions of nucleon excitations are scrutinised to understand their node structure and the underlying role of local interpolating fields in generating the nucleon spectrum. In addressing quark model perspectives, approximately 4000 propagators are employed on the heaviest PACS-CS ensemble at $m_π\simeq$ 702 MeV. We examine the ground and four lowest-lying excited states at zero momentum for both positive- and negative-parity spectra, where the proton's d-quark wavefunction is calculated about the two u quarks at the origin. This is achieved using two local interpolating fields that each carry the quantum numbers of the nucleon but with differing spin-flavour structures, one of which vanishes in the nonrelativistic limit. We find that two distinct types of wavefunction nodes are manifest: "superposition nodes" formed through a linear combination of interpolating fields, and novel "built-in nodes" that are fundamentally built in to the s-wave Dirac components of an individual interpolating field. These are investigated qualitatively through visualisations in the form of both volume and surface renderings, and quantitatively by the calculation of radial wavefunctions. Combined, these findings build a comprehensive picture of the single-particle nucleon spectrum and how its properties derive from fundamental lattice operators.

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arXiv2025

Novel insight into centre-vortex geometry in four dimensions

Centre-vortex surfaces are mapped out in four dimensions within the framework of SU(3) lattice gauge theory to understand the role of secondary loops that develop in three-dimensional visualisations of centre-vortex structure, appearing separate from the percolating cluster. Loops that initially appear disconnected in three-dimensional slices can originate from the same connected surface in four dimensions depending on the surface's curvature. For the first time, these secondary loops are identified as "connected" or "disconnected" with respect to the vortex sheet, allowing new insight into the evolution of centre-vortex geometry through the finite-temperature phase transition. At low temperatures, we find that secondary loops of any length primarily lie in the same sheet percolating the four-dimensional volume. Only a handful of small secondary sheets disconnected from the percolating sheet are identified. Above the phase transition, the vortex structure is still found to be dominated by a single large sheet but one that has aligned with the temporal dimension. With the near absence of any curvature orthogonal to the temporal dimension, connected secondary loops become vanishingly rare. Other novel quantities, such as the four-dimensional density of secondary sheets and the sheet sizes themselves, are analysed to build a complete picture of centre-vortex geometry in four dimensions.

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arXiv2025

Center vortices in the novel phase of staggered fermions

The geometry of center vortices is studied in the novel lattice-artefact phase that appears with staggered fermions to elucidate any insight provided by the center-vortex degrees of freedom. For various numbers of fermion flavors, the single-site shift symmetry of the staggered-fermion action is broken in a finite region of the $(β, m)$ phase space. Simulations are performed with six degenerate fermion flavors and a range of $β$ values that span the phase boundary. Center vortices are demonstrated to capture the broken shift symmetry that manifests in the unphysical phase. This persists at the level of each individual plaquette orientation, where it is revealed that only the plaquettes that span the broken dimension are affected. Several bulk center-vortex quantities, including the vortex and branching point densities, are considered to highlight other aspects of vortex geometry sensitive to the unphysical phase. A slight preference for the plaquettes affected by the broken shift symmetry to be pierced by a vortex is observed. This translates also to a greater branching point density in three-dimensional slices that span the broken dimension. Combined, these findings provide a novel characterization of the unphysical phase in terms of the fundamental center degrees of freedom.

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arXiv2025

Structure of center-vortex matter in SU(4) Yang-Mills theory

The structure of center vortices is studied in SU(4) Yang-Mills theory for the first time to illuminate the interplay between elementary (center charge $\pm 1$) and doubly charged vortices. Unlike in SU(3), where charge $+2$ vortices are simply elementary vortices with reversed orientations in spacetime, these possibilities are physically distinct in SU(4). Visualizations of the vortex structure in three-dimensional slices reveal the various ways in which doubly charged objects manifest, as the convergence and matching of elementary vortices or as isolated doubly charged loops. An algorithm is described to classify every doubly charged chain as one of these three types. A collection of vortex statistics is considered to quantify the vortex structure. Many of these pertain to the novel doubly charged objects, including their relative proportions and chain lengths, which are analyzed to highlight the differences between each chain type. Three different lattice spacings are employed to investigate the approach to the continuum limit. Vortex matching chains are found to be shorter on average but also more prevalent than vortex convergences, ascribed to their interpretation as extended center monopoles. In addition, the lengths of both vortex convergences and vortex matchings are observed to follow an exponential distribution, allowing the introduction of a constant probability for a doubly charged chain to split into two elementary vortices as it propagates. Combined, these findings provide a characterization of the vortices that comprise center-vortex structures in SU(4) Yang-Mills theory.

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arXiv2025

The temperature dependence of fractional topological charge objects

We present a novel method for defining the topological charge contained within distinct topological objects in the nontrivial ground-state fields of SU(N) lattice gauge theory. Such an analysis has been called for by the growing number of models for Yang-Mills topological structure which propose the existence of fractionally charged objects. This investigation is performed for SU(3) at a range of temperatures across the deconfinement phase transition, providing an assessment of how the topological structure evolves with temperature. This reveals a connection between the topological charge and holonomy of the system which must be satisfied by finite-temperature models of Yang-Mills vacuum structure. We find a promising consistency with the instanton-dyon model for SU(N) vacuum structure.

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arXiv2025

SU(3) centre vortex geometry at finite temperature

The importance of examining the structure of centre-vortex matter in the ground-state fields of nonabelian gauge-field theory has been demonstrated in the recent centre-vortex based discovery of a second finite-temperature transition in QCD associated with quark deconfinement. This signals the presence of a new phase of ground-state field structure between the well separated chiral and deconfinement transitions. In this short presentation, we re-examine pure SU(3) gauge theory which provides a foundation for the development of techniques for the examination of full QCD. This time, we reconsider visualisations of the centre-vortex structure in light of the quantitative analysis that demonstrates the first order nature of the deconfinement phase transition in the pure-gauge theory. Here we consider a detailed side-by-side comparison of the field structure slightly below and slightly above the critical temperature. The abrupt changes of the field structure in the first order phase transition are easy to observe in the representative visualisations.

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arXiv2025

Centre vortex evidence for a second finite-temperature QCD transition

Evidence for the existence of a second finite-temperature transition in quantum chromodynamics (QCD) is obtained through the study of centre vortex geometry and its evolution with temperature. The dynamical anisotropic ensembles of the FASTSUM Collaboration are utilised to conduct a comprehensive analysis at eight temperatures beyond the established chiral transition. Visualisations of the centre vortex structure in temporal and spatial slices of the lattice reveal that vortex percolation persists through the chiral transition and ceases at a temperature that is approximately twice the chiral transition temperature $T_c$. This implies that confinement is retained through temperatures up to $T \approx 2\,T_c$, pointing toward a second transition corresponding to deconfinement. The loss of percolation is quantified by the vortex cluster extent, providing a clear signal for the deconfinement transition. Additional vortex statistics, including temporal correlations, vortex and branching point densities, the number of secondary clusters and vortex chain lengths between branching points, are scrutinised as a function of temperature. All ten measures investigated herein show the characteristics of two transitions in QCD, encompassing the chiral transition at $T_c$ and the deconfinement transition at $T \approx 2\,T_c$. Performing an inflection point analysis on the vortex and branching point densities produces an estimate of $T_c$ that agrees with the known FASTSUM value. By the same procedure, a precise estimate of the deconfinement point is extracted as $T_d = 321(6)\,$MeV.

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arXiv2024

Centre vortex geometry at finite temperature

The geometry of centre vortices is studied in $\mathrm{SU(3)}$ gauge theory at finite temperature to capture the key structural changes that occur through the deconfinement phase transition. Visualisations of the vortex structure in temporal and spatial slices of the lattice reveal a preference for the vortex sheet to align with the temporal dimension above the critical temperature. This is quantified through a correlation measure. A collection of vortex statistics, including vortex and branching point densities, and vortex path lengths between branching points, are analysed to highlight internal shifts in vortex behaviour arising from the loss of confinement. We find the zero-temperature inclination of branching points to cluster at short distances vanishes at high temperatures, embodying a rearrangement of branching points within the vortex structure. These findings establish the many aspects of centre vortex geometry that characterise the deconfinement phase transition in pure gauge theory.

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arXiv2024

Numerical evidence for fractional topological objects in SU(3) gauge theory

The continued development of models that propose the existence of fractional topological objects in the Yang-Mills vacuum has called for a quantitative method to study the topological structure of $\mathrm{SU}(N)$ gauge theory. We present an original numerical algorithm that can identify distinct topological objects in the nontrivial ground-state fields and approximate the net charge contained within them. This analysis is performed for $\mathrm{SU(3)}$ colour at a range of temperatures crossing the deconfinement phase transition, allowing for an assessment of how the topological structure evolves with temperature. We find a promising consistency with the instanton-dyon model for the structure of the QCD vacuum at finite temperature. Several other quantities, such as object density and radial size, are also analysed to elicit a further understanding of the fundamental structure of ground-state gluon fields.

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