What question did this study set out to answer?

This research aims to derive explicit expressions for the structure constants in the timelike regime of N=1 Liouville conformal field theory (CFT).

February 27, 2026Journal of High Energy Physics2 citationsOpen Access

On the three-point functions in timelike N = 1 Liouville CFT

BMBeatrix MühlmannETH Zurich VNVladimir NarovlanskyPrinceton University ITIoannis TsiaresCentre National de la Recherche Scientifique

Key Points

This research aims to derive explicit expressions for the structure constants in the timelike regime of N=1 Liouville conformal field theory (CFT).
Utilized analytic superconformal bootstrap methods
Examined structure constants in the timelike regime
Explored shift relations in the NS- and R-sectors
Analyzed normalization-independent bootstrap data on the sphere
Derived timelike structure constants that correspond to spacelike counterparts
Showed agreement between these constants and OPE coefficients of N=1 Minimal Models
Identified implications for constructing the N=1 supersymmetric analog of the Virasoro Minimal String

Abstract

A bstract We use analytic (super-) conformal bootstrap methods to derive explicit expressions for the structure constants of N N = 1 Liouville CFT in the ‘timelike’ regime of the superconformal central charge. The obtained expressions take the form of inverses of the appropriate spacelike counterparts, which we explain concretely by elucidating the analytic properties of the corresponding shift relations in the NS- and R-sectors for the normalization-independent bootstrap data on the sphere. In a particular normalization, the timelike structure constants are shown to agree with the OPE coefficients of N N = 1 Minimal Models when specified at degenerate values of the momenta, exactly as in the non-supersymmetric case. We discuss possible applications of our results, with emphasis on the construction of the N N = 1 supersymmetric analog of the Virasoro Minimal String.

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