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We present a numerical study of a two dimensional model of the Wess-Zumino type. We formulate this model on a sphere, where the fields are expanded in spherical harmonics. The sphere becomes fuzzy by a truncation in the angular momenta. This leads to a finite set of degrees of freedom without explicitly breaking the space symmetries. The corresponding field theory is expressed in terms of a matrix model, which can be simulated. We present first numerical results for the phase structure of a variant of this model on a fuzzy sphere. The prospect to restore exact supersymmetry in certain limits is under investigation.

We present simulation results for the 2-flavour Schwinger model with dynamical Ginsparg-Wilson fermions. Our Dirac operator is constructed by inserting an approximately chiral hypercube operator into the overlap formula, which yields the overlap hypercube operator. Due to the similarity with the hypercubic kernel, a low polynomial of this kernel can be used as a numerically cheap way to evaluate the fermionic part of the Hybrid Monte Carlo force. We verify algorithmic requirements like area conservation and reversibility, and we discuss the viability of this approach in view of the acceptance rate. Next we confirm a high level of locality for this formulation. Finally we evaluate the chiral condensate at light fermion masses, based on the density of low lying Dirac eigenvalues in different topological sectors. The results represent one of the first measurements with dynamical overlap fermions, and they agree very well with analytic predictions.

Institute of Physics, University of Tsukuba,Tsukuba, Ibaraki 305-8571, JapanE-mail:volkholz@physik.hu-berlin.de,bietenho@physik.hu-berlin.de,jnishi@post.kek.jp, susaki@post.kek.jpWe present results of numerical simulations for pure U(1) gauge theory in a non-commutativespace. The theory is mapped onto a dimensionally reduced matrix model, which renders its nu-merical treatment feasible. New data on large lattices reveal the scaling of Wilson loops and theircorrelation functions in the simultaneous limit to the continuum and to infinite volume, at fixednon-commutativity. In this on-goingproject we are particularly interested in the IR behaviour,the“photo-ball” spectrum and in the photon dispersion relation.XXIIIrd International Symposium on Lattice Field Theory25-30 July 2005Trinity College, Dublin, Ireland