Christian Wozar

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 topologic al 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 c ompared to results extracted from Monte-Carlo generated and cooled configurations of the corresponding lattice models. Analyt ical and numerical results are in full agreement and it is demonstrated that the fermionic zero modes are excellent filters for const ituents hidden in fluctuating lattice configurations.

Spectral sums of the Dirac-Wilson operator and their relation to the Polyakov loop

We investigate and compute spectral sums of the Wilson lattice Dirac operator for quenched SU(3) gauge theory. It is demonstrated that there exist sums which serve as order parameters for the confinement-deconfinement phase transition and get their main contribution from the IR end of the spectrum. They are approximately proportional to the Polyakov loop. In contrast to earlier studied spectral sums, some of them are expected to have a well-defined continuum limit.

Supersymmetry Breaking in Low Dimensional Models

Abstract We analyse supersymmetric models that show supersymmetry breaking in one and two dimensions using lattice methods. Starting from supersymmetric quantum mechanics, we explain the fundamental principles and problems that arise in putting supersymmetric models onto the lattice. We compare our lattice results (built upon the non-local SLAC derivative) with numerically exact results obtained within the Hamiltonian approach. A particular emphasis is put on the discussion of boundary conditions. We investigate the ground state structure, mass spectrum, effective potential and Ward identities and conclude that lattice methods are suitable to derive the physical properties of supersymmetric quantum mechanics, even with broken supersymmetry. Based on this result we analyse the two dimensional N = 1 Wess–Zumino model with spontaneous supersymmetry breaking. First we show that (in agreement with earlier analytical and numerical studies) the SLAC derivative is a sensible choice in the quenched model, which is nothing but the two dimensional ϕ 4 model. Then, we present the very first computation of a renormalised critical coupling for the complete supersymmetric model. This calculation makes use of Binder cumulants and is supported by a direct comparison to Ward identity results, both in the continuum and infinite volume limit. The physical picture is completed by masses at two selected couplings, one in the supersymmetric phase and one in the supersymmetry broken phase. Signatures of the goldstino in the fermionic correlator are clearly visible in the broken case.

Inverse Monte-Carlo determination of effective lattice models for SU(3) Yang-Mills theory at finite temperature

This paper concludes our efforts in describing

Phase structure of Z(3)-Polyakov-loop models

SU(3)

Two-dimensional Wess-Zumino models at intermediate couplings

-Yang-Mills theories at different couplings/temperatures in terms of effective Polyakov-loop models. The associated effective couplings are determined through an inverse Monte Carlo procedure based on novel Schwinger-Dyson equations that employ the symmetries of the Haar measure. Because of the first-order nature of the phase transition we encounter a fine-tuning problem in reproducing the correct behavior of the Polyakov-loop from the effective models. The problem remains under control as long as the number of effective couplings is sufficiently small.

Effects of small particle numbers on long-term behaviour in discrete biochemical systems

We study effective lattice actions describing the Polyakov-loop dynamics originating from finite-temperature Yang-Mills theory. Starting with a strong-coupling expansion the effective action is obtained as a series of Z(3)-invariant operators involving higher and higher powers of the Polyakov loop, each with its own coupling. Truncating to a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean-field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches concerning the phase structure of the theories. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic, and antiferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents {nu} and {gamma} at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state Potts model.

Generalized Potts-Models and their Relevance for Gauge Theories ⋆

We consider the two-dimensional N=(2,2) Wess-Zumino model with a cubic superpotential at weak and intermediate couplings. Refined algorithms allow for the extraction of reliable masses in a region where perturbation theory no longer applies. We scrutinize the Nicolai improvement program, which guarantees lattice supersymmetry, and compare the results for ordinary and nonstandard Wilson fermions with those for SLAC derivatives. It turns out that this improvement leads to better results for SLAC fermions but not for Wilson fermions. Furthermore, even without improvement terms the models with all three fermion species reproduce the correct values for the fermion masses in the continuum limit.

Supersymmetric Nonlinear O(3) Sigma Model on the Lattice

Motivation: The functioning of many biological processes depends on the appearance of only a small number of a single molecular species. Additionally, the observation of molecular crowding leads to the insight that even a high number of copies of species do not guarantee their interaction. How single particles contribute to stabilizing biological systems is not well understood yet. Hence, we aim at determining the influence of single molecules on the long-term behaviour of biological systems, i.e. whether they can reach a steady state. Results: We provide theoretical considerations and a tool to analyse Systems Biology Markup Language models for the possibility to stabilize because of the described effects. The theory is an extension of chemical organization theory, which we called discrete chemical organization theory. Furthermore we scanned the BioModels Database for the occurrence of discrete chemical organizations. To exemplify our method, we describe an application to the Template model of the mitotic spindle assembly checkpoint mechanism. Availability and implementation: http://www.biosys.uni-jena.de/Services.html. Contact: bashar.ibrahim@uni-jena.de or dittrich@minet.uni-jena.de Supplementary information: Supplementary data are available at Bioinformatics online.

Z_3 Polyakov loop models and inverse Monte-Carlo methods

We study the Polyakov loop dynamics originating from finite-temperature Yang- Mills theory. The effective actions contain center-symmetric terms involving powers of the Polyakov loop, each with its own coupling. For a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic and antiferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents and at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state spin Potts model. Symmetry constraints and strong coupling expansion for the effective action describing the Polyakov loop dynamics of gauge theories lead to effective field theories with rich phase struc- tures. The fields are the fundamental characters of the gauge group with the fundamental domain as target space. The center symmetry of pure gauge theory remains a symmetry of the effective models. If one further freezes the Polyakov loop to the center Z of the gauge group one obtains the well known vector Potts spin-models, sometimes called clock models. Hence we call the effective theories for the Polyakov loop dynamics generalized Z-Potts models. We review our recent results on generalized Z3-Potts models (1). These results were obtained with the help of an improved mean field approximation and Monte Carlo simulations. The mean field approximation turns out to be much better than expected. Probably this is due to the existence of tricritical points in the effective theories. There exist four distinct phases and transitions of first and second order. The critical exponents and at the second order transition from the symmetric to antiferromagnetic phase for the generalized Potts model are the same as for the