The Kramers–;Wannier Symmetry and S-Duality in the Two-Dimensional g03A6;4 Theory

Abstract

We show that the exact beta function of the two-dimensional gΦ4 theory possesses two dual symmetries. These are the Kramers–Wannier symmetry d(g) and the strong–weak-coupling symmetry, or the S-duality f(g), connecting the strong- and weak-coupling domains lying above and below the fixed point g*. We obtain explicit representations for the functions d(g) and f(g). The S-duality transformation f(g) allows using the high-temperature expansions to approximate the contributions of the higher-order Feynman diagrams. From the mathematical standpoint, the proposed scheme is highly unstable. Nevertheless, the approximate values of the renormalized coupling constant g* obtained from the duality equations agree well with the available numerical results.