The strong-weak coupling symmetry in 2D Φ^4 field models

Abstract

It is found that the exact beta-function β(g) of the continuous 2D gΦ 4 model possesses two types of dual symmetries, these being the KramersWannier (KW) duality symmetry and the strong-weak (SW) coupling symmetry f (g), or S-duality. All these transformations are explicitly constructed. The S-duality transformation f (g) is shown to connect domains of weak and strong couplings, i.e. above and below g * . Basically it means that there is a tempting possibility to compute multiloop Feynman diagrams for the β-function using high-temperature lattice expansions. The regular scheme developed is found to be strongly unstable.Approximate values of the renormalized coupling constant g * found from duality symmetry equations are in an agreement with available numerical results.