Towards the Topological Susceptibility with Overlap Fermions

Using a reweighting technique combined with a low-mode truncation of the fermionic determinant, we estimate the quark-mass dependence of the QCD topological susceptibility with overlap fermions. In contrast to previous lattice simulations which all used non-chiral fermions, our results appear to be consistent with the simple continuum model of Dürr. This indicates that at current lattice spacings the use of the index theorem might not be justified and the fermionic definition of the charge might be needed. Smooth SU(3) gauge field configurations can be characterised with an integer charge Q, a topological invariant. Topology plays a crucial role in shaping the low-energy behavior of QCD. Instantons are believed to be largely responsible for the spontaneous breaking of chiral symmetry. The axial anomaly [1] as well as the large mass of the η′ [2, 3] are also intimately connected to gauge configurations of non-trivial topology. For a good understanding of QCD, it is thus crucial to have a consistent picture of its topological structure. Fluctuations of the topological charge can be characterised with the topological susceptibility,