Benjamin Withers

OPE = QNM

The success of the conformal bootstrap programme has motivated efforts to bootstrap conformal field theories at finite temperature. Temperature introduces a scale, which causes two-point functions of conformal theories exhibit distinct UV and IR regimes. The UV is naturally characterised by thermal operator product expansion (OPE), while the IR is naturally characterised by exponential decay due to quasinormal modes (QNMs). I will show how these two seemingly distinct regimes overlap with each other, allowing us to explicitly relate data appearing in the OPE to data appearing in the QNM expansion, inviting the slogan "OPE=QNM". The outcome is a bootstrap programme where constraints on OPE (such as spectrum of operators) can constrain QNM frequencies, or constraints on QNM frequencies (such as through causality or transport) can constrain OPE spectra. Based on 2607.24909 with P. Arnaudo, C. Iossa, and R. Karlsson.