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Abstract <p>We study semiclassical scattering in Liouville theory, in SL(2,R)/U(1) WZW theory and in SL(3,R) Toda theory, using the relations between the in and out fields defined by the chiral currents of these theories. By these relations we investigate the generating functional F that corresponds to the semiclassical <i>S</i>-matrix. In particular, we construct the Legendre transform of F in a closed form. The construction scheme is similar for these three theories and the obtained functionals have a compact form. This provides a basis for the functional integral representation of the <i>S</i>-matrix in these theories, which earlier was known only for Liouville theory.</p>

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Functional Integral Representation for the S-Matrix in Integrable 2D Conformal Field Theories

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • D. Das,
  • G. Jorjadze,
  • L. Megrelidze

摘要

Abstract

We study semiclassical scattering in Liouville theory, in SL(2,R)/U(1) WZW theory and in SL(3,R) Toda theory, using the relations between the in and out fields defined by the chiral currents of these theories. By these relations we investigate the generating functional F that corresponds to the semiclassical S-matrix. In particular, we construct the Legendre transform of F in a closed form. The construction scheme is similar for these three theories and the obtained functionals have a compact form. This provides a basis for the functional integral representation of the S-matrix in these theories, which earlier was known only for Liouville theory.