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Falk Bruckmann

Publications and source records attributed to Falk Bruckmann.

At least 55 records · Page 3Linked to original sources
arXiv2010

Comparing topological charge definitions using topology fixing actions

We investigate both the hyperbolic action and the determinant ratio action designed to fix the topological charge on the lattice. We show to what extent topology is fixed depending on the parameters of these actions, keeping the physical situation fixed. At the same time the agreement between different definitions of topological charge - the field theoretic and the index definition - is directly correlated to the degree topology is fixed. Moreover, it turns out that the two definitions agree very well. We also study finite volume effects arising in the static potential and related quantities due to topology fixing.

hep-lat↗
arXiv2010

Filtered topological structure of the QCD vacuum: Effects of dynamical quarks

We systematically compare filtering methods used to extract topological structures on SU(3) lattice configurations. We show that there is a strong correlation of the topological charge densities obtained by APE and Stout smearing. To get rid of artifacts of these methods, we analyse structures that are also seen by Laplace filtering and indeed identify artifacts for strong smearing. The topological charge density in this combined analysis is more fragmented in the presence of dynamical quarks. A power law exponent that characterises the distribution of filtered topological clusters turns out to be not far off the values of an instanton gas model.

hep-lat↗
arXiv2009

The Vortex Structure of SU(2) Calorons

We reveal the center vortex content of SU(2) calorons and ensembles of them. We use Laplacian Center Gauge as well as Maximal Center Gauges to show that the vortex in a single caloron consists of two parts. The first one connects the constituent dyons of the caloron (which are monopoles in Laplacian Abelian Gauge) and extends in time. The second part is predominantly spatial, encloses one of the dyons and can be related to the twist in the caloron gauge field. This part depends strongly on the caloron holonomy and degenerates to a plane when the holonomy is maximally nontrivial, i.e. when the asymptotic Polyakov loop is traceless. Correspondingly, we find the spatial vortices in caloron ensembles to percolate in this case. This finding fits perfectly in the confinement scenario of vortices and shows that calorons are suitable to facilitate the vortex confinement mechanism.

hep-th↗
arXiv2009

Vortex Content of SU(2) Calorons and Multi-Calorons

We use Laplacian Center Gauge to reveal the vortex content of single SU(2) calorons and multi-caloron systems at different holonomies. The vortex surfaces in a single SU(2) caloron consist of two parts that are induced by the constituent dyon charges and by the twist between the dyons, respectively. The latter part percolates in a caloron ensemble at maximal nontrivial holonomy. This finding fits perfectly in the confinement scenario of vortices and shows that calorons are suitable to facilitate the vortex confinement mechanism.

hep-lat↗
arXiv2009

Comparing the vacuum structure of quenched and dynamical configurations

We systematically compare filtering methods used to extract topological structures on SU(3) lattice configurations. We show that there is a strong correlation of the topological charge densities obtained by APE and Stout smearing. To get rid of artifacts of these methods, we analyze structures that are also seen by Laplace filtering. This combined analysis shows that the topological charge density is more fragmented in the presence of dynamical quarks.

hep-lat↗
arXiv2009

Fermionic boundary conditions and the finite temperature transition of QCD

Finite temperature lattice QCD is probed by varying the temporal boundary conditions of the fermions. We develop the emerging physical behavior in a study of the quenched case and subsequently present first results for a fully dynamical calculation comparing ensembles below and above the phase transition. We show that for low temperature spectral quantities of the Dirac operator are insensitive to boundary conditions, while in the deconfined phase a non-trivial response to a variation of the boundary conditions sets in.

hep-lat↗
arXiv2009

Cautionary remarks on the moduli space metric for multi-dyon simulations

We perform a detailed numerical investigation of the approximate moduli space metric proposed by Diakonov and Petrov [arXiv:0704.3181] for a confining model of dyons. Our findings strongly indicate that only for a small number of dyons at sufficiently low density this metric is positive definite - and, therefore, a valid moduli space metric - throughout a considerable part of configuration space. This poses strong limitations on results obtained by an unrestricted integration over collective coordinates in this model. It also indicates that strong correlations between collective coordinates will be essential for the physical content of a dyon model, which could be exhibited by a suitable simulation algorithm.

hep-ph↗
arXiv2009

Instanton constituents and fermionic zero modes in twisted CP(n) models

We construct twisted instanton solutions of CP(n) models. Generically a charge-k instanton splits into k(n+1) well-separated and almost static constituents carrying fractional topological charges and being ordered along the noncompact direction. The locations, sizes and charges of the constituents are related to the moduli parameters of the instantons. We sketch how solutions with fractional total charge can be obtained. We also calculate the fermionic zero modes with quasi-periodic boundary conditions in the background of twisted instantons for minimally and supersymmetrically coupled fermions. The zero modes are tracers for the constituents and show a characteristic hopping. The analytical findings are compared to results extracted from Monte-Carlo generated and cooled configurations of the corresponding lattice models. Analytical and numerical results are in full agreement and it is demonstrated that the fermionic zero modes are excellent filters for constituents hidden in fluctuating lattice configurations.

hep-th↗
arXiv2009

How instantons could survive the phase transition

Instantons at finite temperature consist of dyons, with their masses depending on the asymptotic Polyakov loop. It is shown that the suppression of heavy dyons can explain qualitatively the behavior of the periodic and antiperiodic chiral condensate and the topological susceptibility above the phase transition.

hep-ph↗
arXiv2008

Dressed Polyakov loops and center symmetry from Dirac spectra

We construct a novel observable for finite temperature QCD that relates confinement and chiral symmetry. It uses phases as boundary conditions for the fermions. We discuss numerical and analytical aspects of this observable, like its spectral behavior below and above the critical temperature, as well as the connection to chiral condensate and center symmetry.

hep-lat↗
arXiv2008

Generalising the Ginsparg-Wilson relation: Lattice Supersymmetry from Blocking Transformations

The Ginsparg-Wilson relation is extended to interacting field theories with general linear symmetries. Our relation encodes the remnant of the original symmetry in terms of the blocked fields and guides the construction of invariant lattice actions. We apply this approach in the case of lattice supersymmetry. An additional constraint has to be satisfied because of the appearance of a derivative operator in the symmetry transformations. The solution of this constraint leads to non-local SLAC-type derivatives. We investigate the corresponding kinetic operators on the lattice within an exact solution of supersymmetric quantum mechanics. These solutions - analogues of the overlap operator for supersymmetry - can be made local through a specific choice of the blocking kernel. We show that the corresponding relation allows for local lattice symmetry operators as well as local lattice actions. We argue that for interacting theories the lattice action is polynomial in the fields only under special circumstances, which is exemplified within an exact solution.

hep-lat↗
arXiv2008

Generalisations of the Ginsparg-Wilson relation and a remnant of supersymmetry on the lattice

We introduce a lattice symmetry relation for field theories with general linear symmetries. For chiral symmetry the well-known Ginsparg-Wilson relation is reproduced. The new relation encodes the remnant of the original symmetry on the lattice and guides the construction of invariant lattice actions. We apply this approach to lattice supersymmetry. There, an additional constraint has to be satisfied which originates in the derivative operator in the symmetry transformations. As a consequence the non-local SLAC derivative operator appears in the lattice transformation. Despite this non-local form we show how local solutions for quadratic actions can be found. For interacting theories the relation in general leads to a non-polynomial action that can be reduced to a finite polynomial order only under certain conditions.

hep-lat↗
arXiv2008

Dual condensate, dressed Polyakov loops and center symmetry from Dirac spectra

We construct a novel observable for finite temperature QCD that relates confinement and chiral symmetry. It uses phases as boundary conditions for the fermions. We discuss numerical and analytical aspects of this observable, like its spectral behavior below and above the critical temperature, as well as the connection to chiral condensate, center symmetry and the canonical ensemble.

hep-lat↗
arXiv2008

Polyakov loops and spectral properties of the staggered Dirac operator

We study the spectrum of the staggered Dirac operator in SU(2) gauge fields close to the free limit, for both the fundamental and the adjoint representation. Numerically we find a characteristic cluster structure with spacings of adjacent levels separating into three scales. We derive an analytical formula which explains the emergence of these different spectral scales. The behavior on the two coarser scales is determined by the lattice geometry and the Polyakov loops, respectively. Furthermore, we analyze the spectral statistics on all three scales, comparing to predictions from random matrix theory.

hep-lat↗
arXiv2008

Dual quark condensate and dressed Polyakov loops

We construct a new order parameter for finite temperature QCD by considering the quark condensate for U(1)-valued temporal boundary conditions for the fermions. Fourier transformation with respect to the boundary condition defines the dual condensate. This quantity corresponds to an equivalence class of Polyakov loops, thereby being an order parameter for the center symmetry. We explore the duality relation between the quark condensate and these dressed Polyakov loops numerically, using quenched lattice QCD configurations below and above the QCD phase transition. It is demonstrated that the Dirac spectrum responds differently to changing the boundary condition, in a manner that reproduces the expected Polyakov loop pattern. We find the dressed Polyakov loops to be dominated by the lowest Dirac modes, in contrast to thin Polyakov loops investigated earlier.

hep-lat↗
arXiv2008

Polyakov loops and SU(2) staggered Dirac spectra

We consider the spectrum of the staggered Dirac operator with SU(2) gauge fields. Our study is motivated by the fact that the antiunitary symmetries of this operator are different from those of the SU(2) continuum Dirac operator. In this contribution, we investigate in some detail staggered eigenvalue spectra close to the free limit. Numerical experiments in the quenched approximation and at very large $β$-values show that the eigenvalues occur in clusters consisting of eight eigenvalues each. We can predict the locations of these clusters for a given configuration very accurately by an analytical formula involving Polyakov loops and boundary conditions. The spacing distribution of the eigenvalues within the clusters agrees with the chiral symplectic ensemble of random matrix theory, in agreement with theoretical expectations, whereas the spacing distribution between the clusters tends towards Poisson behavior.

hep-lat↗
arXiv2007

Smearing and filtering methods in lattice QCD - a quantitative comparison

We systematically compare three filtering methods used to extract topological excitations from lattice gauge configurations, namely smearing, Laplace filtering and the filtered fermionic topological charge (with chirally improved fermions). Each of these techniques introduces ambiguities, like its parameter dependence. We show, however, that all these methods can be tuned to each other over a broad range of filtering levels and that they reveal very similar topological structures. For these common structures we find an interesting power-law relating the number and packing fraction of clusters of filtered topological charge.

hep-lat↗
arXiv2007

Quantitative comparison of filtering methods in lattice QCD

We systematically compare filtering methods used to extract topological excitations (like instantons, calorons, monopoles and vortices) from lattice gauge configurations, namely APE-smearing and spectral decompositions based on lattice Dirac and Laplace operators. Each of these techniques introduces ambiguities, which can invalidate the interpretation of the results. We show, however, that all these methods, when handled with care, reveal very similar topological structures. Hence, these common structures are free of ambiguities and faithfully represent infrared degrees of freedom in the QCD vacuum. As an application we discuss an interesting power-law for the clusters of filtered topological charge.

hep-lat↗