arXiv subjects

W. Bietenholz

Publications and source records attributed to W. Bietenholz.

At least 55 records · Page 3Linked to original sources

arXiv2003

Spectral Properties of the Overlap Dirac Operator in QCD

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at β= 5.85 and β= 6. We distinguish the topological sectors and study the distributions of the leading non-zero eigenvalues, which are stereographically mapped onto the imaginary axis. Thus they can be compared to the predictions of random matrix theory applied to the ε-expansion of chiral perturbation theory. We find a satisfactory agreement, if the physical volume exceeds about (1.2 fm)^{4}. For the unfolded level spacing distribution we find an accurate agreement with the random matrix conjecture on all volumes that we considered.

hep-lat↗

arXiv2003

The Non-Commutative λϕ^{4} Model

In the recent years, field theory on non-commutative (NC) spaces has attracted a lot of attention. Most literature on this subject deals with perturbation theory, although the latter runs into grave problems beyond one loop. Here we present results from a fully non-perturbative approach. In particular, we performed numerical simulations of the λϕ^{4} model with two NC spatial coordinates, and a commutative Euclidean time. This theory is lattice discretized and then mapped onto a matrix model. The simulation results reveal a phase diagram with various types of ordered phases. We discuss the suitable order parameters, as well as the spatial and temporal correlators. The dispersion relation clearly shows a trend towards the expected IR singularity. Its parameterization provides the tool to extract the continuum limit.

hep-th↗

arXiv2003

Numerical results on the Non-commutative λϕ^4 Model

The UV/IR mixing in the λϕ^4 model on a non-commutative (NC) space leads to new predictions in perturbation theory, including Hartree-Fock type approximations. Among them there is a changed phase diagram and an unusual behavior of the correlation functions. In particular this mixing leads to a deformation of the dispersion relation. We present numerical results for these effects in d=3 with two NC coordinates.

hep-th↗

arXiv2003

Extracting physics from an unphysical situation: light mesons in a small box

Quantum Chromo Dynamics is considered in a setup where the light mesons are squeezed into unphysically small boxes. We show how such a situation can be used to determine the couplings of the low energy chiral Lagrangian from lattice simulations, applying chirally invariant formulations of lattice fermions.

physics.comp-ph↗

arXiv2003

Dimensional Reduction of Fermions in Brane Worlds of the Gross-Neveu Model

We study the dimensional reduction of fermions, both in the symmetric and in the broken phase of the 3-d Gross-Neveu model at large N. In particular, in the broken phase we construct an exact solution for a stable brane world consisting of a domain wall and an anti-wall. A left-handed 2-d fermion localized on the domain wall and a right-handed fermion localized on the anti-wall communicate with each other through the 3-d bulk. In this way they are bound together to form a Dirac fermion of mass m. As a consequence of asymptotic freedom of the 2-d Gross-Neveu model, the 2-d correlation length ξ= 1/m increases exponentially with the brane separation. Hence, from the low-energy point of view of a 2-d observer, the separation of the branes appears very small and the world becomes indistinguishable from a 2-d space-time. Our toy model provides a mechanism for brane stabilization: branes made of fermions may be stable due to their baryon asymmetry. Ironically, our brane world is stable only if it has an extreme baryon asymmetry with all states in this ``world'' being completely filled.

hep-th↗

arXiv2003

Simulations in the epsilon-Regime of Chiral Perturbation Theory

We discuss the potential of Ginsparg-Wilson fermion simulations in the epsilon-regime of chiral perturbation theory, regarding the determination of the leading low energy constants of the effective chiral Lagrangian. It turns out to be very hard to measure observables in the topologically trivial sector. There a huge statistics would be required, due to the frequent occurrence of very small eigenvalues. Moreover, contact with chiral perturbation theory is only established if the physical volume of the system is sufficiently large.

hep-lat↗

arXiv2003

Random Matrix Theory and the Spectra of Overlap Fermions

The application of Random Matrix Theory to the Dirac operator of QCD yields predictions for the probability distributions of the lowest eigenvalues. We measured Dirac operator spectra using massless overlap fermions in quenched QCD at topological charge ν= 0, +- 1 and +- 2, and found agreement with those predictions - at least for the first non-zero eigenvalue - if the volume exceeds about (1.2 fm)^4.

hep-lat↗

arXiv2003

Naturally Light Fermions from Dimensional Reduction

We consider the 3-d Gross-Neveu model in the broken phase and construct a stable brane world by means of a domain wall and an anti-wall. Fermions of opposite chirality are localized on the walls and coupled through the 3-d bulk. At large wall separation βthe 2-d correlation length diverges exponentially, hence a 2-d observer cannot distinguish this situation from a 2-d space-time. The 3-d 4-fermion coupling and βfix the effective 2-d coupling such that the asymptotic freedom of the 2-d model arises. This mechanism provides criticality without fine tuning.

hep-lat↗

arXiv2003

A Ginsparg-Wilson Approach to Lattice Chern-Simons Theory

The concept of lattice modified symmetry formulations is adapted to the parity symmetry of gauge fields and applied to the pure Abelian Chern-Simons action in three dimensions. We derive an analogue of the Ginsparg-Wilson relation for the parity anti-symmetry, which is motivated from the perfect lattice action, and which we denote as the Chern-Simons-Ginsparg-Wilson relation (CSGWR). In addition to the overlap type solutions, we construct explicitly simple and local polynomial solutions to the CSGWR. We show that these actions are exactly invariant under a lattice modified parity transformation. That transformation is local as well, and it turns into the standard parity transformation in the continuum limit.

hep-lat↗

arXiv2002

Non--Commutative Field Theories beyond Perturbation Theory

We investigate two models in non-commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally reduced matrix models. Using this technique, we measure Wilson loops in 2d NC gauge theory of rank 1. It turns out that they are non-perturbatively renormalizable, and the phase follows an Aharonov-Bohm effect if we identify θ= 1/B. Next we study the 3d λϕ^{4} model with two NC coordinates, where we present new results for the correlators and the dispersion relation. We further reveal the explicit phase diagram. The ordered regime splits into a uniform and a striped phase, as it was qualitatively conjectured before. We also confirm the recent observation by Ambjorn and Catterall that such stripes occur even in d=2, although they imply the spontaneous breaking of translation symmetry. However, in d=3 and d=2 we observe only patterns of two stripes to be stable in the range of parameters investigated.

hep-th↗

arXiv2002

A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane

We perform a non-perturbative study of pure gauge theory in a two dimensional non-commutative (NC) space. On the lattice, it is equivalent to the twisted Eguchi-Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large-N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point function of Polyakov lines. The 2-point functions agree with a universal wave function renormalization. Based on a Morita equivalence, the large-N double scaling limit corresponds to the continuum limit of NC gauge theory, so the observed large-N scaling demonstrates the non-perturbative renormalizability of this NC field theory. The area law for the Wilson loops holds at small physical area as in commutative 2d planar gauge theory, but at large areas we find an oscillating behavior instead. In that regime the phase of the Wilson loop grows linearly with the area. This agrees with the Aharonov-Bohm effect in the presence of a constant magnetic field, identified with the inverse non-commutativity parameter.

hep-th↗

arXiv2002

Chern-Simons theory on the lattice

We present new proposals for the representation of a Chern-Simons term on the lattice. In the first part, such a term is constructed from the fermion determinant, and in the second part directly from the Abelian gauge term. In both cases, the parity transformation is modified on the lattice without affecting its continuum limit.

hep-lat↗

arXiv2002

Simulating non-commutative field theory

Non-commutative (NC) field theories can be mapped onto twisted matrix models. This mapping enables their Monte Carlo simulation, where the large N limit of the matrix models describes the continuum limit of NC field theory. First we present numeric results for 2d NC gauge theory of rank 1, which turns out to be renormalizable. The area law for the Wilson loop holds at small area, but at large area we observe a rotating phase, which corresponds to an Aharonov-Bohm effect. Next we investigate the NC phi^4 model in d=3 and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d=4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns.

hep-lat↗

arXiv2002

Convergence Rate and Locality of Improved Overlap Fermions

We construct new Ginsparg-Wilson fermions for QCD by inserting an approximately chiral Dirac operator - which involves ingredients of a perfect action - into the overlap formula. This accelerates the convergence of the overlap Dirac operator by a factor of 5 compared to the standard construction, which inserts the Wilson fermion as a point of departure. Taking into account the effort for treating the improved fermion, we are left with an total computational overhead of about a factor 3. This remaining factor is likely to be compensated by other virtues; here we show that the level of locality is clearly improved, so that the exponent of the correlation decay is doubled. We also show that approximate rotation invariance is drastically improved, but a careful scaling test has to be postponed.

hep-lat↗

arXiv2002

Contents of Lattice 2001 Proceedings

We give here the contents pages for the Proceedings of the Lattice 2001 conference (19th International Symposium on Lattice Field Theory) that took place in August 2001 in Berlin, Germany. The contents are in HTML form with clickable links to the papers that exist on the arXiv, mostly in hep-lat. Corrections and comments should be sent to bunk@physik.hu-berlin.de.

hep-lat↗

arXiv2001

The Area Law in Matrix Models for Large N QCD Strings

We study the question whether matrix models obtained in the zero volume limit of 4d Yang-Mills theories can describe large N QCD strings. The matrix model we use is a variant of the Eguchi-Kawai model in terms of Hermitian matrices, but without any twists or quenching. This model was originally proposed as a toy model of the IIB matrix model. In contrast to common expectations, we do observe the area law for Wilson loops in a significant range of scale of the loop area. Numerical simulations show that this range is stable as N increases up to 768, which strongly suggests that it persists in the large N limit. Hence the equivalence to QCD strings may hold for length scales inside a finite regime.

hep-lat↗

arXiv2001

Fast evaluation and locality of overlap fermions

In order to construct improved overlap fermions, we start from a short ranged approximate Ginsparg-Wilson fermion and insert it into the overlap formula. We show that its polynomial evaluation is accelerated considerably compared to the standard Neuberger fermion. In addition the degree of locality is strongly improved.

hep-lat↗

arXiv2001

On the Quantum Geometry of String Theory

The IKKT or IIB matrix model has been proposed as a non-perturbative definition of type IIB superstring theories. It has the attractive feature that space--time appears dynamically. It is possible that lower dimensional universes dominate the theory, therefore providing a dynamical solution to the reduction of space--time dimensionality. We summarize recent works that show the central role of the phase of the fermion determinant in the possible realization of such a scenario.

hep-lat↗