This article is cited in 2 papers

The Kramers–Wannier Symmetry and $S$-Duality in the Two-Dimensional $g\Phi ^4$ Theory

B. N. Shalaev<sup>abc

a</sup> Ioffe Physico-Technical Institute, Russian Academy of Sciences
^b INFN — National Institute of Nuclear Physics, Sezione di Pavia
^c Max Planck Institute for Solid State Research

Abstract: We show that the exact beta function of the two-dimensional $g\Phi ^4$ 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.

Received: 05.10.2001

DOI: 10.4213/tmf325

 English version: Theoretical and Mathematical Physics, 2002, 131:2, 621–628

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