arXiv subjects

M. Quandt

Publications and source records attributed to M. Quandt.

At least 37 records · Page 2Linked to original sources

arXiv2011

Stable charged cosmic strings

We study the quantum stabilization of a cosmic string by a heavy fermion doublet in a reduced version of the standard model. We show that charged strings, obtained by populating fermionic bound state levels, become stable if the electro--weak bosons are coupled to a fermion that is less than twice as heavy as the top quark. This result suggests that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model. Numerically we find the most favorable string profile to be a simple "trough" in the Higgs vev of radius $\approx 10^{-18}\,\mathrm{m}$. The vacuum remains stable in our model, because neutral strings are not energetically favored.

hep-th↗

arXiv2011

Testing Proposals for the Yang-Mills Vacuum Wavefunctional by Measurement of the Vacuum

We review a method, suggested many years ago, to numerically measure the relative amplitudes of the true Yang-Mills vacuum wavefunctional in a finite set of lattice-regulated field configurations. The technique is applied in 2+1 dimensions to sets of abelian plane wave configurations of varying amplitude and wavelength, and sets of non-abelian constant configurations. The results are compared to the predictions of several proposed versions of the Yang-Mills vacuum wavefunctional that have appeared in the literature. These include (i) a suggestion in temporal gauge due to Greensite and Olejnik; (ii) the "new variables" wavefunction put forward by Karabali, Kim, and Nair; (iii) a hybrid proposal combining features of the temporal gauge and new variables wavefunctionals; and (iv) Coulomb gauge wavefunctionals developed by Reinhardt and co-workers, and by Szczepaniak and co-workers. We find that wavefunctionals which simplify to a "dimensional reduction" form at large scales, i.e. which have the form of a probability distribution for two-dimensional lattice gauge theory, when evaluated on long-wavelength configurations, have the optimal agreement with the data.

hep-lat↗

arXiv2011

Hamiltonian approach to Yang-Mills theory in Coulomb gauge - revisited

I briefly review results obtained within the variational Hamiltonian approach to Yang-Mills theory in Coulomb gauge and confront them with recent lattice data. The variational approach is extended to non-Gaussian wave functionals including three- and four-gluon kernels in the exponential of the vacuum wave functional and used to calculate the three-gluon vertex. A new functional renormalization group flow equation for Hamiltonian Yang--Mills theory in Coulomb gauge is solved for the gluon and ghost propagator under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.

hep-th↗

arXiv2010

Vortex characterisation of frustration in the 2d Ising spin glass

The frustrated Ising model on a two-dimensional lattice with open boundary conditions is revisited. A hidden Z2 gauge symmetry relates models with different frustrations which, however, share the same partition function. By means of a duality transformation, it is shown that the partition function only depends on the distribution of gauge invariant vortices on the lattice. We finally show that the exact ground state energy can be calculated in polynomial time using Edmonds' algorithm.

cond-mat.dis-nn↗

arXiv2010

Propagators in lattice Coulomb gauge and confinement mechanisms

We discuss the gluon propagator in 3- and 4-dimensional Yang-Mills theories in Coulomb gauge and compare it with the corresponding Landau gauge propagator, showing that for both the relevant IR mass scale coincides. We also report preliminary results on Coulomb gauge ghost form factor and quark propagators and give a comment on the gluon propagator's strong coupling limit.

hep-lat↗

arXiv2010

Gauge Invariance and Vacuum Energies of Non-Abelian String-Configurations

We improve on a method to compute the fermion contribution to the vacuum polarization energy of string-like configurations in a non-Abelian gauge theory. We establish the new method by numerically verifying the invariance under (a subset of) local gauge transformations. This also provides further support for the use of spectral methods to compute vacuum polarization energies in general. We confirm that the vacuum energy in the MS-bar renormalization scheme is tiny as compared to the mass of the fluctuating fermion field. Numerical results for the physical on-shell scheme are also presented.

hep-th↗

arXiv2010

BRST symmetry vs. Horizon condition in Yang-Mills theories

We show that in SU(2) Yang-Mills theories a simple relation exists between lattice gluon propagators in Coulomb and Landau gauge and discuss the physical implications of such result. In particular, the realization of the Gribov-Zwanziger confinement mechanism in Coulomb gauge, linked to dual-superconductivity, would imply that the standard BRST charge must be ill defined non perturbatively. As a consequence, the Kugo-Ojima confinement criterion, which relies on BRST charge conservation beyond perturbation theory, would not be fulfilled.

hep-lat↗

arXiv2010

Vacuum Energies of Non--Abelian String--Configurations in 3+1 Dimensions

We develop a method to compute the fermion contribution to the vacuum polarization energy of string--like configurations in a non--abelian gauge theory. This calculation has been hampered previously by a number of technical obstacles. We use gauge invariance of the energy and separation of length scales in the energy density to overcome these obstacles. We present a proof-of-principle investigation that shows that this energy is small in the MS-bar renormalization scheme. The generalization to other schemes is straightforward.

hep-th↗

arXiv2010

The role of center vortices in Gribov's confinement scenario

The connection of Gribov's confinement scenario in Coulomb gauge with the center vortex picture of confinement is investigated. For this purpose we assume a vacuum wave functional which models the infrared properties of the theory and in particular shows strict confinement, i.e. an area law of the Wilson loop. We isolate the center vortex content of this wave functional by standard lattice methods and investigate their contributions to various static propagators of the Hamilton approach to Yang-Mills theory in Coulomb gauge. We find that the infrared properties of these quantities, in particular the infrared divergence of the ghost form factor, are dominated by center vortices.

hep-lat↗

arXiv2009

Hamiltonian approach to Yang-Mills theory in Coulomb gauge

I review results recently obtained within the Hamiltonian approach to Yang-Mills theory in Coulomb gauge. In particular, I will present results for the ghost and gluon propagators and compare these with recent lattice data. Furthermore, I will give an interpretation of the inverse of the ghost form factor as the dielectric function of the Yang-Mills vacuum. Our ansatz for the vacuum wave functional will be checked by means of functional renormalization group flow equations, which are solved for the gluon energy and the ghost form factor. Finally, we calculate the Wilson loop for the vacuum wave functional obtained from the variational approach, using a Dyson equation.

hep-th↗

arXiv2008

The gluon propagator in Coulomb gauge from the lattice

We show that in the lattice Hamiltonian limit the static transverse propagator $D(|\vec{p}|)\propto\int d p_0 D(|\vec{p}|,p_0)$ satisfies multiplicative renormalizability. We give a procedure to calculate $D(|\vec{p}|)$ on available lattices at finite temporal spacing. The result agrees at all momenta with the Gribov formula $D(|\vec{p}|)\propto(|\vec{p}|^2+ M^4 |\vec{p}|^{-2})^{-{1/2}}$, with $M=0.88(1) {\rm GeV} \simeq 2 \sqrtσ$.

hep-lat↗

arXiv2008

Coulomb gauge ghost propagator and the Coulomb potential

The ghost propagator and the Coulomb potential are evaluated in Coulomb gauge on the lattice, using an improved gauge fixing scheme which includes the residual symmetry. This setting has been shown to be essential in order to explain the scaling violations in the instantaneous gluon propagator. We find that both the ghost propagator and the Coulomb potential are insensitive to the Gribov problem or the details of the residual gauge fixing, even if the Coulomb potential is evaluated from the A0--propagator instead of the Coulomb kernel. In particular, no signs of scaling violations could be found in either quantity, at least to well below the numerical accuracy where these violations were visible for the gluon propagator. The Coulomb potential from the A0-propagator is shown to be in qualitative agreement with the (formally equivalent) expression evaluated from the Coulomb kernel.

hep-th↗

arXiv2008

Coulomb gauge gluon propagator and the Gribov formula

We analyze the lattice SU(2) Yang-Mills theory in Coulomb gauge. We show that the static gluon propagator is multiplicative renormalizable and takes the simple form $D(|\vec{p}|)^{-1}=\sqrt{|\vec{p}|^2+M^4/|\vec{p}|^2}$, proposed by Gribov through heuristic arguments many years ago. We find $M=0.88(1) {\rm GeV} \simeq 2 \sqrtσ$.

hep-lat↗

arXiv2008

Recent results from the Hamiltonian approach to Yang-Mills theory in Coulomb gauge

Within the Hamiltonian approach to Yang-Mills theory in Coulomb gauge the ghost and gluon propagators are determined from a variational solution of the Yang-Mills Schroedinger equation showing both gluon and heavy quark confinement. The continuum results are in good agreement with lattice data. The ghost form factor is identified as the dielectric function of the Yang--Mills vacuum and the Gribov-Zwanziger confinement scenario is shown to imply the dual Meissner effect. The topological susceptibility is calculated.

hep-th↗

arXiv2007

Quantum stabilization of Z-strings, a status report on D=3+1 dimensions

We investigate an extension to the phase shift formalism for calculating one-loop determinants. This extension is motivated by requirements of the computation of Z-string quantum energies in D=3+1 dimensions. A subtlety that seems to imply that the vacuum polarization diagram in this formalism is (erroneously) finite is thoroughly investigated.

hep-th↗

arXiv2007

Localization of overlap modes and topological charge, vortices and monopoles in SU(3) LGT

We present selected recent results of the QCDSF collaboration on the localization and dimensionality of low overlap eigenmodes and of the topological density in the quenched SU(3) vacuum. We discuss the correlations between the topological structure revealed by overlap fermions without filtering and the confining monopole and P-vortex structure obtained in the Indirect Maximal Center Gauge.

hep-lat↗

arXiv2007

Coulomb gauge Green functions and Gribov copies in SU(2) lattice gauge theory

We reconsider the lattice measurement of Green functions in Coulomb gauge, both in 2+1 and 3+1 dimensions, using an improved gauge fixing scheme. The influence of Gribov copies is examined and we find clear indications that Green functions are more strongly affected than previously assumed, in particular for low momenta. Qualitatively, our improved lattice results in the infra-red compare more favourably with recent continuum calculations in the Hamiltonian approach.

hep-lat↗

arXiv2006

Quantum Energies of Strings in a 2+1 Dimensional Gauge Theory

We study classically unstable string type configurations and compute the renormalized vacuum polarization energies that arise from fermion fluctuations in a 2+1 dimensional analog of the standard model. We then search for a minimum of the total energy (classical plus vacuum polarization energies) by varying the profile functions that characterize the string. We find that typical string configurations bind numerous fermions and that populating these levels is beneficial to further decrease the total energy. Ultimately our goal is to explore the stabilization of string type configurations in the standard model through quantum effects. We compute the vacuum polarization energy within the phase shift formalism which identifies terms in the Born series for scattering data and Feynman diagrams. This approach allows us to implement standard renormalization conditions of perturbation theory and thus yields the unambiguous result for this non--perturbative contribution to the total energy.

hep-th↗