Ernst-Michael Ilgenfritz

First evidence for the existence of instantons in the quantized SU(2) lattice vacuum

Starting from Monte Carlo generated equilibrium gauge field configurations at β = 2.1 and 2.2 on a 64 lattice, representing the pysical vacuum, we systematically freeze the quantum fluctuations by means of successive relaxations. The result is that we obtain (approximate) solutions of the classical equations of motion, which turn out to have discrete values of the action nS ≈ β2π2N, N = 0, 1, 2,… n. in close agreement with the continuum (multi-) instanton solutions. We show that these “lattice (multi-) instantons” are localized in space-time, that they carry a topological charge |Q| = N and that they give rise to a number of fermion zero modes in accordance with the Atiyah-Singer index theorem. Finally, we estimate the “background topological susceptibility” from the distribution of lattice (multi-) instantons.

The finite-temperature phase transition in lattice SU(2) Higgs theory at weak couplings

Abstract In the weak-coupling region, at β = 8 and a λ corresponding to an intermediate Higgs mass, the Higgs transition is studied on asymmetric thermal ( N σ 3 ×2) lattices. A two-state signal is identified, indicating a first-order transition. Multihistogram and finite-size analysis are consistent wich such a conclusion although the evidence is rather weak. The value of the Higgs condensate v ( T crit ) indicates a weakly first-order transition, in qualitive accordance with partially resummed perturbation theory. On the other hand, the latent heat and the metastability temperature range σT / T crit exceed perturbative estimates by an order of magnitude. Higgs and vector boson masses are measured on symmetric lattices near the zero-temperature phase transition. The W-mass is found to be more sensitive to the lattice size than the Higgs mass. Masses and condensates are consistent with improved tree level relations within reasonable renormalized couplings.

Lattice studies at zero and finite temperature in the SU(2) Higgs model at small couplings

Abstract In the weak coupling region ( β =8, λ =0.0017235 and 0.023705) the Higgs transition is determined on symmetrical (16 4 ) as well as thermal (16 3 × N τ ) lattices. This transition is weakly first order and becomes weaker for larger λ. Higgs and vector boson masses are obtained near to the phase transition, consistent with a mass ratio depending on λ only. The transition temperature is obtained as a function of the Higgs mass. The results are compared with perturbative relations.

The lattice SU(2) confining string as an Abrikosov vortex

Abstract Numerical data [K. Schilling, G.S. Bali, C. Schlichter, Prog. Theor. (Proc. Suppl.) 131 (1998) 645; Nucl. Phys. (Proc. Suppl.) 63 (1998) 519; 73 (1999) 638] for the SU(2) confining string in the maximal abelian projection are analysed. The distribution of the electric flux and monopole currents are perfectly described by the classical equations of motion for the dual Abelian Higgs model. The mass of the vector boson is equal to the mass of the monopole (Higgs particle) within numerical errors. The classical energy per unit length of the Abrikosov vortex reproduces 94% of the full non-Abelian string tension.Numerical data for the SU(2) confining string in the maximal abelian projection are analysed. The distribution of the electric flux and monopole currents are perfectly described by the classical equations of motion for the dual Abelian Higgs model. The mass of the vector boson is equal to the mass of the monopole (Higgs particle) within numerical errors. The classical energy per unit length of the Abrikosov vortex reproduces 94% of the full non-Abelian string tension.

QUARK-INDUCED CORRELATIONS BETWEEN INSTANTONS DRIVE THE CHIRAL PHASE TRANSITION

Abstract A simple model for the instanton ensemble at finite temperature is proposed, including a random and stronly correlated molecular component. The temperature dependence of fermionic zero modes naturally leads to chiral symmetry restoration, without instanton suppression. Moreover, at temperatures near and above the transition temperature, the non-perturvative effects due to instanton molecules are so strong that they even dominate the global thermodynamics.

A Numerical reinvestigation of the Aoki phase with N(f) = 2 Wilson fermions at zero temperature

We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose the Hybrid Monte Carlo algorithm was used and an explicit symmetry-breaking source term

3D lattice simulation of the electroweak phase transition at small Higgs mass

hbar{psi} i gamma_{5} tau^{3}psi

Statistical bootstrap of fireball decay spectra

was added to the Wilson fermion action. The order parameter

Thermal QCD transition with two flavors of twisted mass fermions

langlebar{psi}igamma_{5}tau^{3}psirangle

Quantum number conservation in the statistical bootstrap of fireball decay spectra

was studied at several values of