Critical comparison of different definitions of topological charge on the lattice - art. no. 114506

A detailed comparison is made between the field-theoretic and geometric def initions of topological charge density on the lattice. Their renormalizatio ns with respect to the continuum are analyzed. The definition of the topolo gical susceptibility chi, as used in chiral Ward identities, is reviewed. A fter performing the subtractions required by it, the different lattice meth ods yield results in agreement with each other. The methods based on coolin g and on counting fermionic zero modes are also discussed. [S0556-2821(98)1 0921-9].