BPST instanton

The dx¹⊗σ₃ coefficient of BPST instanton on the (x¹,x²)-slice of R⁴ where σ₃ is the third Pauli matrix (top left). The dx²⊗σ₃ coefficient (top right). These coefficients A₁³ and A₂³ determine the restriction of the BPST instanton A with g=2,ρ=1,z=0 to this slice. The corresponding field strength centered around z=0 (bottom left). A visual representation of the field strength of a BPST instanton with center z on the compactification S⁴ of R⁴ (bottom right).

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.^[1] It is a classical solution to the equations of motion of SU(2) Yang–Mills theory in Euclidean space-time (i.e. after Wick rotation), meaning it describes a transition between two different topological vacua of the theory. It was originally hoped to open the path to solving the problem of confinement, especially since Polyakov had proven in 1975 that instantons are the cause of confinement in three-dimensional compact-QED.^[2] This hope was not realized, however.