# The imaginary Toda field theory

Abstract : We consider the two-dimensional $\mathfrak{sl}_n$ quantum Toda field theory with an imaginary background charge. This conformal field theory has a higher spin symmetry ($W_n$ algebra), a central charge $c \leq n-1$ and a continuous spectrum. Using the conformal bootstrap, we compute structure constants involving two arbitrary scalar fields and a semi-degenerate field of Wyllard type. The solution obtained is not the analytic continuation of the usual Toda three-point function. Non-scalar primary fields and their three-point functions are also discussed. Non-scalar primary fields are classified by conjugacy classes of the permutation group $\mathfrak{S}_n$, and their structure constants are computed explicitly, up to an overall factor.
Keywords :
Type de document :
Pré-publication, Document de travail
2018
Domaine :

https://hal.archives-ouvertes.fr/hal-01886110
Contributeur : Inspire Hep <>
Soumis le : mardi 2 octobre 2018 - 15:40:10
Dernière modification le : mardi 9 octobre 2018 - 14:18:53

### Citation

Thomas Dupic, Benoît Estienne, Yacine Ikhlef. The imaginary Toda field theory. 2018. 〈hal-01886110〉

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