Emergent Inert Adjoint Scalar Field in SU(2) Yang-Mills Thermodynamics due to Coarse-Grained Topological Fluctuations

Figure 2

Possible directions of winding of (𝜙/|𝜙|)(𝜏) around the group manifold 𝑆³ of SU(2). The angles 𝛾,𝛿 are arbitrary but constant. They are determined by the choice of plane in which angular regularization is carried out when computing 𝜙’s phase, see below. The angle 𝛼(𝜏) parametrizes the 𝑆¹ winding of 𝜙/|𝜙|.