Spatial 't Hooft loop to cubic order in hot QCD

Spatial 't Hooft loops of strength k measure the qualitative change in the behaviour of electric colour flux in confined and deconfined phase of SU(N) gauge theory. They show an area law in the deconfined phase, known analytically to two loop order with a “k-scaling” law k(N−k). In this paper we compute the O(g3) correction to the tension. It is due to neutral gluon fields that get their mass through interaction with the wall. The simple k-scaling is lost in cubic order. The generic problem of nonconvexity shows up in this order and the cure is provided. The result for large N is explicitly given. We show that nonperturbative effects appear at O(g5).