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September 10, 2025Open Access

Three-point correlation functions in the sl₃ Toda theory II: The Fateev–Litvinov formula

Key Points

The fateev-litvinov formula reveals features of three-point correlation functions in toda CFTs, enhancing understanding of their structure.
This research draws upon probabilistic methods alongside techniques taken from the physics literature, leading to novel integrability results.
By connecting to the famed DOZZ formula in Liouville CFT, this finding illuminates the broader mathematical landscape of conformal field theories.
Results highlight how toda theories, represented by liouville CFT analogs, display intricate symmetry through associated lie algebras.

Abstract

Toda conformal field theories (CFTs) form a family of two-dimensional CFTs indexed by semisimple and complex Lie algebras. One of their remarkable features is that they are natural generalizations of Liouville CFT that enjoy an enhanced level of symmetry, prescribed by W -algebras. They likewise admit a probabilistic formulation in terms of Gaussian multiplicative chaos. Based on this probabilistic framework, this second article in a two-part series is dedicated to providing a first step towards integrability of these theories. In this perspective, we prove the Fateev–Litvinov formula for a family of three-point correlation functions associated to the sl₃ Toda CFT. This result is the analog of the celebrated DOZZ formula in Liouville CFT. Our method of proof features techniques inspired by the physics literature together with probabilistic ones that naturally arise within the setting of Toda theories.

Three-point correlation functions in the sl₃ Toda theory II: The Fateev–Litvinov formula

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Abstract

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