Improved cooling algorithm for gauge theories

As a method to eliminate UV noise and permit studying topological excitations cooling must fulfill certain requirements: smooth out the short range fluctuations, including “dislocations” preserve the structure at the physical scales, including size and location of instantons ensure stability of the cooled structures need no monitoring or any engineering which could make it configuration dependent or would only slow it down without ensuring stability. Since Wilson action has no stable instantons (they shrink and decay under cooling) one usually attempts to calibrate or engineer the cooling procedure based on it such as to obtain metastability, after the noise has been reduced but before the instantons shrank to zero. This, however, makes cooling more an art than a method and also does not answer the question of preserving the physical scales of the original configuration. A general tree level analysis of various actions [1] distinguishes between “under improved” (e.g., Wilson) and “over improved” ones; under the former instantons shrink, under the latter instantons beyond a certain size grow [1,2]. We here consider the problem of “improved” cooling algorithms which ensure a high degree of scale invariance for the instantons beyond the short range scale. They