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G. Münster

Publications and source records attributed to G. Münster.

At least 19 recordsLinked to original sources
arXiv2015

Witten index and phase diagram of compactified N=1 supersymmetric Yang-Mills theory on the lattice

Owing to confinement, the fundamental particles of N=1 Supersymmetric Yang-Mills (SYM) theory, gluons and gluinos, appear only in colourless bound states at zero temperature. Compactifying the Euclidean time dimension with periodic boundary conditions for fermions preserves supersymmetry, and confinement is predicted to persist independently of the length of the compactified dimension. This scenario can be tested non-perturbatively with Monte-Carlo simulations on a lattice. SUSY is, however, broken on the lattice and can be recovered only in the continuum limit. The partition function of compactified N=1 SYM theory with periodic fermion boundary conditions corresponds to the Witten index. Therefore it can be used to test whether supersymmetry is realized on the lattice. Results of our recent numerical simulations are presented, supporting the disappearance of the deconfinement transition in the supersymmetric limit and the restoration of SUSY at low energies.

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arXiv2015

First studies of the phase diagram of N=1 supersymmetric Yang-Mills theory

The behavior of supersymmetric theories at finite temperatures differs from that of other theories in certain aspects. Due to the different thermal statistics of bosons and fermions, supersymmetry is explicitly broken for any non-zero value of the temperature. We study N=1 supersymmetric Yang-Mills theory on the lattice at finite temperatures. This model is the simplest supersymmetric extension of the pure gauge sector of QCD, describing the interactions between gluons and their fermionic superpartners, the gluinos. At zero temperature the theory confines like QCD, and chiral symmetry is spontaneously broken. At high temperatures, deconfinement and chiral symmetry restoration are expected to take place, but it is not known whether these two phase transitions coincide or not. First results on this topic, obtained in numerical simulations on the lattice, will be presented and discussed.

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arXiv2014

Phase structure of the N=1 supersymmetric Yang-Mills theory at finite temperature

Supersymmetry (SUSY) has been proposed to be a central concept for the physics beyond the standard model and for a description of the strong interactions in the context of the AdS/CFT correspondence. A deeper understanding of these developments requires the knowledge of the properties of supersymmetric models at finite temperatures. We present a Monte Carlo investigation of the finite temperature phase diagram of the N=1 supersymmetric Yang-Mills theory (SYM) regularised on a space-time lattice. The model is in many aspects similar to QCD: quark confinement and fermion condensation occur in the low temperature regime of both theories. A comparison to QCD is therefore possible. The simulations show that for N=1 SYM the deconfinement temperature has a mild dependence on the fermion mass. The analysis of the chiral condensate susceptibility supports the possibility that chiral symmetry is restored near the deconfinement phase transition.

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arXiv2013

Clover fermions in the adjoint representation and simulations of supersymmetric Yang-Mills theory

Clover improvement is the standard choice for lattice simulations of QCD, when the lattice artefacts coming from Wilson fermions have to be reduced. However, the clover improvement is not limited to QCD, but can be applied to a wider range of theories with fermions in higher representations of the gauge group SU(N), like the adjoint fermions required by supersymmetry or by technicolor theories. We present the calculation of the clover coefficient up to one loop order with standard perturbation theory for these models. Applications of clover fermions to supersymmetric Yang-Mills theory are also discussed.

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arXiv2010

Simulation of 4d N=1 supersymmetric Yang-Mills theory with Symanzik improved gauge action and stout smearing

We report on the results of a numerical simulation concerning the low-lying spectrum of four-dimensional N=1 SU(2) Supersymmetric Yang-Mills (SYM) theory on the lattice with light dynamical gluinos. In the gauge sector the tree-level Symanzik improved gauge action is used, while we use the Wilson formulation in the fermion sector with stout smearing of the gauge links in the Wilson-Dirac operator. The ensembles of gauge configurations were produced with the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) updating algorithm. We performed simulations on large lattices up to a size of 24^3 x 48 at $β=1.6$. Using QCD units with the Sommer scale being set to r_0 = 0.5 fm, the lattice spacing is about a ~ 0.09 fm, and the spatial extent of the lattice corresponds to 2.1 fm. At the lightest simulated gluino mass the spin-1/2 gluino-glue bound state appeared to be considerably heavier than its expected super-partner, the pseudoscalar bound state. Whether supermultiplets are formed remains to be studied in upcoming simulations.

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arXiv2009

Monte Carlo approach to turbulence

The behavior of the one-dimensional random-force-driven Burgers equation is investigated in the path integral formalism on a discrete space-time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as structure functions, as ensemble averages over different field realizations. The regularization of shock solutions to the zero-viscosity limit (Hopf-equation) eventually leads to constraints on lattice parameters required for the stability of the simulations. Insight into the formation of localized structures (shocks) and their dynamics is obtained.

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arXiv2009

Simulations of supersymmetric Yang-Mills theory

Results of a numerical simulation concerning the low-lying spectrum of four-dimensional N=1 SU(2) Supersymmetric Yang-Mills (SYM) theory on the lattice with light dynamical gluinos are reported. We use the tree-level Symanzik improved gauge action and Wilson fermions with stout smearing of the gauge links in the Wilson-Dirac operator. The configurations are produced with the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) algorithm. We performed simulations on lattices up to a size of 24^3x48 at β=1.6. Using QCD units with the Sommer scale being set to r_0=0.5 fm, the lattice spacing is about a~0.09 fm, and the spatial extent of the lattice corresponds to 2.1 fm to control finite size effects. At the lightest simulated gluino mass our results indicate a mass for the lightest gluino-glue bound state, which is considerably heavier than the values obtained for its possible superpartners. Whether supermultiplets are formed remains to be studied in upcoming simulations.

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arXiv2008

Dynamical simulation of lattice 4d N=1 SYM

The lattice provides a powerful tool to non-perturbatively investigate strongly coupled supersymmetric Yang-Mills (SYM) theories. The pure SU(2) SYM theory with one supercharge is simulated on large lattices with small Majorana gluino masses down to about $am_{\tilde g}=0.068$ with lattice spacing $a\simeq 0.125$ fm. The gluino dynamics is simulated by the Two-Step Multi-Boson (TSMB) and the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) algorithms. Supersymmetry (SUSY) is broken explicitly by the lattice and the Wilson term and softly by the presence of a non-vanishing gluino mass. However, the recovery of SUSY is expected in the infinite volume continuum limit by tuning the bare parameters to the SUSY point in the parameter space. This scenario is studied by the determination of the low-energy mass spectrum and by means of lattice SUSY Ward-Identities (WIs).

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arXiv2008

Dynamical Twisted Mass Fermions with Light Quarks: Simulation and Analysis Details

In a recent paper [hep-lat/0701012] we presented precise lattice QCD results of our European Twisted Mass Collaboration (ETMC). They were obtained by employing two mass-degenerate flavours of twisted mass fermions at maximal twist. In the present paper we give details on our simulations and the computation of physical observables. In particular, we discuss the problem of tuning to maximal twist, the techniques we have used to compute correlators and error estimates. In addition, we provide more information on the algorithm used, the autocorrelation times and scale determination, the evaluation of disconnected contributions and the description of our data by means of chiral perturbation theory formulae.

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arXiv2008

Spectrum of 4d N=1 SYM on the lattice with light dynamical Wilson gluinos

We perform Monte Carlo investigations of the 4d ${\cal N}=1$ supersymmetric Yang-Mills (SYM) theory on the lattice with dynamical gluinos in the adjoint representation of the SU(2) gauge group. Our aim is to determine the mass spectrum of the low-lying bound states which is expected to be organised in supermultiplets in the infinite volume continuum limit. For this purpose we perform simulations on large lattices, up to an extension $L/r_0 \simeq 6$ where $r_0 \simeq 0.5 \rm fm$ is the Sommer scale parameter. We apply improved lattice actions: tree-level improved Symanzik (tlSym) gauge action and in the later runs a Stout-smeared Wilson fermion action. The gauge configuration samples are prepared by the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) update algorithm.

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arXiv2008

Hadron spectrum of QCD with one quark flavor

The latest results of an ongoing project for the lattice simulation of QCD with a single quark flavor are presented. The Symanzik tree-level-improved Wilson action is adopted in the gauge sector and the (unimproved) Wilson action for the fermion. Results from new simulations with one step of Stout-smearing (rho=0.15) in the fermion action are discussed. The one-flavor theory is simulated by a polynomial hybrid Monte Carlo algorithm (PHMC) at beta=4.0 corresponding to a = 0.13fm, on 16^3x32 and 24^3x48 lattices; the box-size is L = 2.1fm and L = 3.1fm, respectively. At the lightest simulated quark mass the (partially quenched) pion mass is ~300 MeV. The masses of the lightest bound states are computed, including the flavor singlet scalar and pseudoscalar mesons sigma_s and eta_s, the scalar glueball 0^++, and the Delta^++ baryon. Relics of SUSY in the mass spectrum, expected from a large N_c orientifold equivalence with the N=1 supersymmetric Yang-Mills theory, are discussed.

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arXiv2008

Monte Carlo simulations of the randomly forced Burgers equation

The behaviour of the one--dimensional random--forced Burgers equation is investigated in the path integral formalism, using a discrete space--time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as structure functions, as ensemble averages over different field realizations. The regularization of shock solutions to the zero--viscosity limit (Hopf-eq.) eventually leads to constraints on lattice parameters, required for the stability of the simulations. Insight into the formation of localized structures (shocks) and their dynamics is obtained.

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arXiv2007

Strong coupling expansion for Yang-Mills theory at finite temperature

Euclidean strong coupling expansion of the partition function is applied to lattice Yang-Mills theory at finite temperature, i.e. for lattices with a compactified temporal direction. The expansions have a finite radius of convergence and thus are valid only for $β<β_c$, where $β_c$ denotes the nearest singularity of the free energy on the real axis. The accessible temperature range is thus the confined regime up to the deconfinement transition. We have calculated the first few orders of these expansions of the free energy density as well as the screening masses for the gauge groups SU(2) and SU(3). The resulting free energy series can be summed up and corresponds to a glueball gas of the lowest mass glueballs up to the calculated order. Our result can be used to fix the lower integration constant for Monte Carlo calculations of the thermodynamic pressure via the integral method, and shows from first principles that in the confined phase this constant is indeed exponentially small. Similarly, our results also explain the weak temperature dependence of glueball screening masses below $T_c$, as observed in Monte Carlo simulations. Possibilities and difficulties in extracting $β_c$ from the series are discussed.

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arXiv2007

Hadron masses in QCD with one quark flavour

One-flavour QCD - a gauge theory with SU(3) colour gauge group and a fermion in the fundamental representation - is studied by Monte Carlo simulations. The mass spectrum of hadronic bound states is investigated in a volume with extensions of L ~ 4.4r_0 (~2.2fm) at two different lattice spacings: a ~ 0.37r_0 (~0.19fm) and a ~ 0.27r_0 (~0.13fm). The lattice action is Symanzik tree-level-improved Wilson action for the gauge field and (unimproved) Wilson action for the fermion.

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arXiv2004

The Volume Source Technique for flavor singlets: a second look

We reconsider the Volume Source Technique (VST) for the determination of flavor singlet quantities on the lattice. We point out a difficulty arising in the case of fermions in real representations of the gauge group and propose an improved version of the method (IVST) based on random gauge transformations of the background configuration. We compare the performance of IVST with the method based on stochastic estimators (SET). We consider the case of the N=1 Supersymmetric Yang-Mills Theory (SYM), where just one fermionic flavor is present, the gluino in the adjoint representation, and only flavor singlet states are possible. The work is part of an inclusive analysis of the spectrum of the lightest particles of the theory, based on the simulation of the model on a $16^3\cdot32$ lattice with dynamical gluinos in the Wilson scheme.

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