出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：The use of adjoint (quasi) zero-modes of the Dirac operator to probe the Yangs-Mills vacuum has
been recently advocated by González-Arroyo and Kirchner. The construction relies on the use
of the super-symmetric zero mode which, for classical configurations, provides a direct estimate
of the gauge action density. In the lattice implementation of this idea, we show how the results
improve considerably if the overlap operator is used instead of the Wilson-Dirac one. Before
proceeding to the detailed study ofMonte Carlo ensembles, we studied here a series of potentially
complicated situations which can be encountered. In particular, we study the case of instanton
anti-instanton pairs and analyse how the results depend upon separation. The effect of lattice
artifacts is also of concern. Indeed, a statistical analysis of zero modes of thermalised SU(2)
configurations at b = 2.57 shows a significant fraction having 4N +2 adjoint zero modes, in
contradiction with the index theorem. This violation must be associated to the roughness of the
lattice configurations. Indeed, we show that this situation occurs for instantons of size of the order
of the lattice spacing.
