63 research outputs found
Width of the flux tube in compact U(1) gauge theory in three dimensions
We study the squared width and the profile of flux tubes in compact U(1)
lattice gauge theory in three spacetime dimensions. The results obtained from
numerical calculations in the dual formulation of this confining theory are
compared with predictions from an effective bosonic-string model and from the
dual-superconductor model: it is found that the former fails at describing the
quantitative features of the flux tube, while the latter is in good agreement
with Monte Carlo data. The analytical interpretation of these results (in the
light of the semi-classical analysis by Polyakov) is pointed out, and a
comparison with non-Abelian gauge theories in four spacetime dimensions is
discussed.Comment: 19 pages, 5 pdf figures; v2: 21 pages, 8 pdf figures: references
added, new data and new figures included, discussion slightly revise
Fine structure of the confining string in an analytically solvable 3D model
In lattice gauge theory in three spacetime dimensions,
confinement can be analytically shown to persist at all values of the coupling.
Furthermore, the explicit predictions for the dependence of string tension
and mass gap on the coupling allow one to tune their ratio at
will. These features, and the possibility of obtaining high-precision numerical
results via an exact duality map to a spin model, make this theory an ideal
laboratory to test the effective string description of confining flux tubes. In
this contribution, we discuss our investigation of next-to-leading-order
corrections to the confining potential and of the finite-temperature behavior
of the flux tube width. Our data provide a very stringent test of the
theoretical predictions for these quantities and allow to test their dependence
on the ratio.Comment: Presented at the 31st International Symposium on Lattice Field Theory
(Lattice 2013), 29 July - 3 August 2013, Mainz, German
A different kind of string
In U(1) lattice gauge theory in three spacetime dimensions, the problem of
confinement can be studied analytically in a semi-classical approach, in terms
of a gas of monopoles with Coulomb-like interactions. In addition, this theory
can be mapped to a spin model via an exact duality transformation, which allows
one to perform high-precision numerical studies of the confining potential.
Taking advantage of these properties, we carried out an accurate investigation
of the effective string describing the low-energy properties of flux tubes in
this confining gauge theory. We found striking deviations from the expected
Nambu-Goto-like behavior, and, for the first time, evidence for contributions
that can be described by a term proportional to the extrinsic curvature of the
effective string worldsheet. Such term is allowed by Lorentz invariance, and
its presence in the infrared regime of the U(1) model was indeed predicted by
Polyakov several years ago. Our results show that this term scales as expected
according to Polyakov's solution, and becomes the dominant contribution to the
effective string action in the continuum limit. We also demonstrate
analytically that the corrections to the confining potential induced by the
extrinsic curvature term can be related to the partition function of the
massive perturbation of a c=1 bosonic conformal field theory. The implications
of our results for SU(N) Yang-Mills theories in three and in four spacetime
dimensions are discussed.Comment: 1+21 pages, 2 figures; v2 (1+24 pages, 2 figures): improved the
discussion in the conclusions' section, added an appendix, included new
references, updated the affiliation details for one of the authors, corrected
typos: version published in the journa
Effective string description of the interquark potential in the 3D U(1) lattice gauge theory
The U(1) lattice gauge theory in three dimensions is a perfect laboratory to
study the properties of the confining string. On the one hand, thanks to the
mapping to a Coulomb gas of monopoles, the confining properties of the model
can be studied semi-classically. On the other hand, high-precision numerical
estimates of Polyakov loop correlators can be obtained via a duality map to a
spin model. This allowed us to perform high-precision tests of the universal
behavior of the effective string and to find macroscopic deviations with
respect to the expected Nambu-Goto predictions. These corrections could be
fitted with very good precision including a contribution (which is consistent
with Lorentz symmetry) proportional to the square of the extrinsic curvature in
the effective string action, as originally suggested by Polyakov. Performing
our analysis at different values of we were able to show that this term
scales as expected by Polyakov's solution and dominates in the continuum. We
also discuss the interplay between the extrinsic curvature contribution and the
boundary correction induced by the Polyakov loops.Comment: 7 pages, 2 pdf figures, contribution to the 32nd International
Symposium on Lattice Field Theory "Lattice 2014" (23-28 June 2014, Columbia
University, New York, NY, USA
Squared width and profile of the confining flux tube in the U(1) LGT in 3D
The dual formulation of the compact U(1) lattice gauge theory in three
spacetime dimensions allows to finely study the squared width and the profile
of the confining flux tube on a wide range of physical interquark distances.
The results obtained in Monte Carlo simulations are compared with the
predictions of the effective bosonic-string model and with the dual
superconductor model. While the former fails at describing the data from a
quantitative point of view, the latter is in good agreement with it. An
interpretation of these results is proposed in light of the particular features
of the U(1) lattice gauge theory in 3D and a comparison with non-Abelian gauge
theories in four spacetime dimensions is discussed.Comment: 7 pages, 2 figures,Talk presented at the 34th International Symposium
on Lattice Field Theory (Lattice 2016), 24-30 July 2016, Southampton, U
Out-of-equilibrium simulations to fight topological freezing
Calculations of topological observables in lattice gauge theories with
traditional Monte Carlo algorithms have long been known to be a difficult task,
owing to the effects of long autocorrelations times. Several mitigation
strategies have been put forward, including the use of open boundary conditions
and methods such as parallel tempering. In this contribution we examine a new
approach based on out-of-equilibrium Monte Carlo simulations. Starting from
thermalized configurations with open boundary conditions on a line defect,
periodic boundary conditions are gradually switched on. A sampling of
topological observables is then shown to be possible with a specific
reweighting-like technique inspired by Jarzynski's equality. We discuss the
efficiency of this approach using results obtained for the 2-dimensional
models. Furthermore, we outline the implementation of our
proposal in the context of Stochastic Normalizing Flows, as they share the same
theoretical framework of the non-equilibrium transformations we perform, and
can be thought of as their generalization.Comment: 1+8 pages, 6 figures, contribution for the 40th International
Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th,
2023, Fermi National Accelerator Laborator
Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
We study the high-temperature phase of compact U(1) gauge theory in 2+1
dimensions, comparing the results of lattice calculations with analytical
predictions from the conformal-field-theory description of the low-temperature
phase of the bidimensional XY model. We focus on the two-point correlation
functions of probe charges and the field-strength operator, finding excellent
quantitative agreement with the functional form and the continuously varying
critical indices predicted by conformal field theory.Comment: 1+26 pages, 4 figures; v2: 1+31 pages, 4 figure
The quenched glueball spectrum from smeared spectral densities
The standard approach to compute the glueball spectrum on the lattice relies
on the evaluation of effective masses from two-point correlation functions of
operators with the quantum numbers of the desired state. In this work, we
propose an alternative procedure, based on the numerical computation of smeared
spectral densities. Even though the extraction of the latter from lattice
correlators is a notoriously ill-posed inverse problem, we show that a recently
developed numerical method, based on the Backus-Gilbert regularization,
provides a robust way to evaluate a smeared version of the spectral densities.
Fitting the latter to a combination of Gaussians, we extract the masses of the
lightest glueball and of its first excitation in the spectrum of the theory.
While the preliminary results presented in this contribution are restricted to
simulations at finite lattice spacing and finite volume, and for the purely
gluonic sector of QCD, they represent the first step in a systematic
investigation of glueballs using spectral-reconstruction methods.Comment: 10 pages, 3 figures, contribution to the 40th International Symposium
on Lattice Field Theory, 31st of July - 4th of August, 2023, Fermilab,
Batavia, U.S.
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