arXiv subjects

L. E. Oxman

Publications and source records attributed to L. E. Oxman.

At least 19 recordsLinked to original sources

arXiv2026

Thick oriented and nonoriented center-vortex $SU(N)$ configurations with fractional topological charge lumps

Mixed oriented and nonoriented center vortices are known to generate nontrivial topological charge. However, most previous analyses have been restricted to Abelian-projected thin configurations. Studies of thick vortices have so far focused on the $SU(2)$ case and on the intersection of a single pair of oriented objects. In this work, we construct mixed oriented and nonoriented thick center-vortex gauge fields in $SU(N)$ with smooth profiles and explicit non-Abelian phases. These phases ensure a smooth interpolation between different Cartan fluxes at monopole junctions. We analyze the resulting topological charge density and visualize its morphology, elucidating the color structures responsible for fractional lumps that together yield a nonvanishing global charge.

hep-th↗

arXiv2026

The 't Hooft loop from a center-vortex wave functional

Previously, we proposed an infrared vacuum wave functional for $SU(N)$ Yang-Mills theory peaked at thin center vortices and showed that it yields an area law for the Wilson loop. In this work, we use this wave functional to calculate the spatial 't Hooft loop, for which we find a perimeter law, in accordance with 't Hooft's criterion for confinement.

hep-th↗

arXiv2025

Ensembles of center vortices and chains: Insights from a natural lattice framework

A scenario to understand the asymptotic properties of confinement between quark probes, based on a 4D mixed ensemble of percolating center-vortex worldsurfaces and chains, was initially proposed by one of us in a non-Abelian setting. More recently, the same physics was reobtained by means of a Schrödinger wavefunctional peaked at Abelian-projected configurations, which deals with center-vortex lines and pointlike monopoles in real space. In this work, we formulate the Abelian-projected ensemble and reassess the non-Abelian one within the Weingarten lattice representation for the sum over surfaces. In the phase where worldsurfaces are stabilized by contact interactions and percolate, lattice gauge fields emerge. This generalizes the Goldstone modes in an Abelian loop condensate to the case where non-Abelian degrees of freedom are present. In this language, the different natural matching properties of elementary center-vortex worldsurfaces and monopole worldlines can be easily characterized. In the lattice, the Abelian setting also implements the original idea that the mixed ensemble reconciles $N$-ality with the formation of a confining flux tube. In this picture, center vortices and chains explain why Abelian-projected variables capture this property at asymptotic distances while simultaneously allowing for a 'dual superconductor' description of the fundamental string. Common features, differences in the continuum, and perspectives will also be addressed.

hep-th↗

arXiv2022

The infrared Yang-Mills wave functional due to percolating center vortices

Inspired by the center-vortex dominance in the infrared sector of $SU(N)$ Yang-Mills theory observed on the lattice, we propose a vacuum wave functional localized on an ensemble of correlated center vortices endowed with stiffness and magnetic monopoles that change the orientation of the vortex flux. In the electric-field representation, this wave functional becomes an effective partition function for N complex scalar fields. The inclusion of both oriented and non-oriented vortices as well as so-called N-vortex matchings leads to an effective potential that has only a center symmetry left. In the center-vortex condensed phase, this symmetry is spontaneously broken. In this case, the Wilson loop average can be approximated by a solitonic saddle-point localized around the minimal surface. The asymptotic string tension thus obtained displays Casimir scaling.

hep-th↗

arXiv2021

Renormalizability of a first principles Yang-Mills center-vortex ensemble

Recently, a new procedure to quantize the $SU(N)$ Yang-Mills theory in the nonperturbative regime was proposed. The idea is to divide the configuration space $\{A_μ\}$ into sectors labeled by different topological degrees of freedom and fix the gauge separately on each one of them. As Singer's theorem on gauge copies only refers to gauge fixing conditions that are global in $\{A_μ\}$, this construction might avoid the Gribov problem. In this work, we present a proof of the renormalizability in the center-vortex sectors, thus establishing the calculability of the Yang-Mills center-vortex ensemble.

hep-th↗

arXiv2021

From center-vortex ensembles to the confining flux tube

In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang-Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modelling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the nonoriented center-vortex component and non-Abelian degrees when modelling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

hep-th↗

arXiv2020

Study of Gribov Copies in the Yang-Mills ensemble

Recently, based on a new procedure to quantize the theory in the continuum, it was argued that Singer's theorem points towards the existence of a Yang-Mills ensemble. In the new approach, the gauge fields are mapped into an auxiliary field space used to separately fix the gauge on different sectors labeled by center vortices. In this work, we study this procedure in more detail. We provide examples of configurations belonging to sectors labeled by center vortices and discuss the existence of nonabelian degrees of freedom. Then, we discuss the importance of the mapping injectivity, and show that this property holds infinitesimally for typical configurations of the vortex-free sector and for the simplest example in the one-vortex sector. Finally, we show that these configurations are free from Gribov copies.

hep-th↗

arXiv2020

BPS strings and the stability of the asymptotic Casimir law in adjoint flavor-symmetric YMH models

We investigate an effective flavor-symmetric Yang-Mills-Higgs model with $N^2-1$ adjoint scalar fields. We find a set of BPS equations that provide vortex solutions and calculate their energies for arbitrary representations. We show that, for a given N-ality $k$, the energy of the corresponding antisymmetric representation is the lowest. This completes the proof that this model is able to reproduce a Casimir law for the string tension at asymptotic distances.

hep-th↗

arXiv2020

Renormalizability of the center-vortex free sector of Yang-Mills theory

In this work, we analyzed a recent proposal to detect $SU(N)$ continuum Yang-Mills sectors labeled by center vortices, inspired by Laplacian-type center gauges in the lattice. Initially, after the introduction of appropriate external sources, we obtained a rich set of sector-dependent Ward identities, which can be used to control the form of the divergences. Next, we were able to show the all-order multiplicative renormalizability of the center-vortex free sector. These are important steps towards the establishment of a first principles, well-defined, and calculable Yang-Mills ensemble.

hep-th↗

arXiv2019

3D Yang-Mills confining properties from a non-Abelian ensemble perspective

In this work, we propose a $3D$ ensemble measure for center-vortex worldlines and chains equipped with non-Abelian degrees of freedom. We derive an effective field description for the center-element average where the vortices get represented by $N$ flavors of effective Higgs fields transforming in the fundamental representation. This field content is required to accommodate fusion rules where $N$ vortices can be created out of the vacuum. The inclusion of the chain sector, formed by center-vortex worldlines attached to pointlike defects, leads to a discrete set of $Z(N)$ vacua. This type of SSB pattern supports the formation of a stable domain wall between quarks, thus accommodating not only a linear potential but also the Lüscher term. Moreover, after a detailed analysis of the associated field equations, the asymptotic string tension turns out to scale with the quadratic Casimir of the antisymmetric quark representation. These behaviors reproduce those derived from Monte Carlo simulations in $SU(N)$ $3D$ Yang-Mills theory, which lacked understanding in the framework of confinement as due to percolating magnetic defects.

hep-th↗

arXiv2019

Quantum effects due to a moving Dirichlet point

We study quantum effects induced by a point-like object that imposes Dirichlet boundary conditions along its world-line, on a real scalar field $φ$ in 1, 2 and 3 spatial dimensions. The boundary conditions result from the strong coupling limit of a term quadratic in the field and localized on the particle's trajectory. We discuss the renormalization issues that appear and evaluate the effective action. Special attention is paid to the case of 2 spatial dimensions where the coupling constant is adimensional.

hep-th↗

arXiv2019

Pattern revivals from fractional Gouy phases in structured light

We investigate pattern revivals in specially designed optical structures that combine different transverse modes. In general, the resulting pattern is not preserved under free propagation and gets transformed due to non synchronized Gouy phases. However, it is possible to build structures in which the Gouy phases synchronize at specific fractional values, thus recovering the initial pattern at the corresponding longitudinal positions. This effect is illustrated with a radially structured light spot in which the beam energy can be addressed to different positions without the need of intermediate optical components, what can be useful for optical communications and optical tweezing with structured beams.

physics.optics↗

arXiv2018

4D ensembles of percolating center vortices and chains

In this work, we review a recently proposed measure to compute center-element averages in a mixed ensemble of center vortices and chains with non-Abelian d.o.f. and monopole fusion. When center vortices percolate and monopoles condense, the average is captured by a saddle point and collective modes in a YMH model. In this manner, the Lüscher term, confining flux tubes with N-ality and confined gluons were accommodated in an ensemble picture.

hep-th↗

arXiv2018

$k$-Strings with exact Casimir law and Abelian-like profiles

We explore vortex solutions for a class of dual $SU(N)$ Yang-Mills models with $N^2-1$ Higgs fields in the adjoint representation. Initially, we show that there is a collective behavior that can be expressed in terms of a small $N$-independent number of field profiles. Then, we find a region in parameter space where the nontrivial profiles coincide with those of the Nielsen-Olesen vortex, and the energy scales exactly with the quadratic Casimir. Out of this region, we solve the ansatz equations numerically and find very small deviations from the Casimir law. The coexistence of Abelian-like string profiles and non-Abelian scaling features is welcome, as these properties have been approximately observed in pure YM lattice simulations.

hep-th↗

arXiv2018

4d ensembles of percolating center vortices and monopole defects: the emergence of flux tubes with N-ality and gluon confinement

Ensembles of magnetic defects represent quantum variables that have been detected and extensively explored in lattice ${\rm SU}(N)$ pure Yang-Mills theory. They successfully explain many properties of confinement and are strongly believed to capture the (infrared) path-integral measure. In this work, we initially motivate the presence of magnetic non-Abelian degrees of freedom in these ensembles. Next, we consider a simple Gaussian model to account for fluctuations. In this case, both center vortices and monopoles become relevant degrees in Wilson loop averages. These physical inputs are then implemented in an ensemble of percolating center vortices in four dimensions by proposing a measure to compute center-element averages. The introduction of phenomenological information such as monopole tension, stiffness, and fusion leads to an effective YMH model with adjoint Higgs fields. If monopoles also condense, then the gauge group undergoes ${\rm SU}(N) \to {\rm Z}(N)$ SSB. This pattern has been proposed as a strong candidate to describe confinement. In the presence of external quarks, these models are known to be dominated by classical solutions, formed by flux tubes with $N$-ality as well as by confined dual monopoles (gluons).

hep-th↗

arXiv2017

Effective theory of the D = 3 center vortex ensemble

By means of lattice calculations, center vortices have been established as the infrared dominant gauge field configurations of Yang-Mills theory. In this work, we investigate an ensemble of center vortices in D = 3 Euclidean space-time dimension where they form closed flux loops. To account for the properties of center vortices detected on the lattice, they are equipped with tension, stiffness and a repulsive contact interaction. The ensemble of oriented center vortices is then mapped onto an effective theory of a complex scalar field with a U(1) symmetry. For a positive tension, small vortex loops are favoured and the Wilson loop displays a perimeter law while for a negative tension, large loops dominate the ensemble. In this case the U(1) symmetry of the effective scalar field theory is spontaneously broken and the Wilson loop shows an area law. To account for the large quantum fluctuations of the corresponding Goldstone modes, we use a lattice representation, which results in an XY model with frustration, for which we also study the Villain approximation.

hep-th↗

arXiv2017

Intrinsic bounds of a two-qudit random evolution

We investigate entangled qudits evolving under random, local $SU(d)$ operations and demonstrate that this evolution is constrained by intrinsic bounds, showing robust features of two-qudit entangled states that can be useful for fault tolerant implementations of phase gates. Our analytical results are supported by numerical simulations and confirmed by experiments on liquid-state nuclear magnetic resonance qubits.

quant-ph↗

arXiv2017

Experimental observation of fractional topological phases with photonic qudits

Geometrical and topological phases play a fundamental role in quantum theory. Geometric phases have been proposed as a tool for implementing unitary gates for quantum computation. A fractional topological phase has been recently discovered for bipartite systems. The dimension of the Hilbert space determines the topological phase of entangled qudits under local unitary operations. Here we investigate fractional topological phases acquired by photonic entangled qudits. Photon pairs prepared as spatial qudits are operated inside a Sagnac interferometer and the two-photon interference pattern reveals the topological phase as fringes shifts when local operations are performed. Dimensions $d = 2, 3$ and $4$ were tested, showing the expected theoretical values.

quant-ph↗