Scale anomaly induced instanton interaction

The binary interaction of large size instantons in a SU(2) Yang-Mills theory is obtained from the one-loop effective action for the field strength. The instanton interaction is calculated as a function of the instanton separation and in dependence on radius and relative orientation of the instantons. Two equally oriented instantons with radii large compared with the scale defined by the gluon condensate have purely attractive interaction, whereas the interaction of maximal disoriented instantons is repulsive. We argue that the medium range attractive interaction of the instantons generally holds and is solely due to the instability of the perturbative vacuum. 1 Supported by DFG under contract Re 856/1 − 2 1 1. Introduction The confidence in QCD as the correct theory of strong interactions stems from the excellent agreement between QCD predictions and high energy scattering experiments [1]. This success, from a theoretical point of view, is due to QCD's remarkable property of asymptotic freedom [1], which implies that physics, involving high momentum transfers, can be described in a perturbative expansion with respect to the coupling. At low energy, however, the running coupling constant is expected to be large implying that a study of the QCD ground state is beyond the scope of perturbation theory. For this reason only a few aspects of the QCD vacuum are known up to now. An important property is that scale invariance of pure Yang-Mills theory is anomalously broken by quantum fluctuations [2] indicated by a non-vanishing value for the gluon condensate. In this context instantons [3] play an important role for describing the QCD vacuum, since they give rise to a gluon condensate. Furthermore instantons may possibly trigger spontaneous breaking of chiral symmetry [4] and offer an explanation of the U A (1) problem [5]. Instantons are gauge field configurations which minimise the euclidean Yang Mills action and correspond to localised spots of self-or antiself-dual field strength. Investigations of the interaction between instantons, originating from the classical Yang-Mills action, show that the gluonic vacuum is not realised as a dilute gas of instantons [4], but rather than an instanton liquid [6, 7, 8]. Recent investigations which include shape variations of the instantons indicate that instantons might lose their identity in a strongly correlated instanton medium [9]. Instantons have a free scale parameter, the instanton radius, which reflects the scale invariance of the classical Yang Mills action. If the effects of fluctuations around the instanton …