BPST instanton

Type of Yang–Mills instanton

In theoretical physics, the BPST instanton is the instanton with winding number 1 found by Alexander Belavin, Alexander Polyakov, Albert Schwarz and Yu. S. Tyupkin. This hope was not realized, however.

It is expected that BPST like instantons play an important role in the vacuum structure of QCD. Instantons are indeed found in lattice calculations. The first computations performed with instantons used the dilute gas approximation. The results obtained did not solve the infrared problem of QCD, making many physicists turn away from instanton physics. Later, though, an instanton liquid model was proposed, turning out to be a more promising approach. The dilute instanton gas model departs from the supposition that the QCD vacuum consists of a gas of BPST instantons. Although only the solutions with one or few instantons (or anti instantons) are known exactly, a dilute gas of instantons and anti instantons can be approximated by considering a superposition of one instanton solutions at great distances from one another. 't Hooft calculated the effective action for such an ensemble, and he found an infrared divergence for big instantons, meaning that an infinite amount of infinitely big instantons would populate the vacuum. Later, an instanton liquid model was studied. This model starts from the assumption that an ensemble of instantons cannot be described by a mere sum of separate instantons. Various models have been proposed, introducing interactions between instantons or using variational methods (like the "valley approximation") endeavouring to approximate the exact multi instanton solution as closely as possible. Many phenomenological successes have been reached. These are not local minima of the action, but instead they correspond to saddle points. Instantons are also closely related to merons, singular non dual solutions of the Euclidean Yang–Mills field equations of topological charge 1/2. Instantons are thought to be composed of two merons.