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The dynamics of multi-kaon systems are of relevance for several areas ofnuclear physics. However, even the simplest systems, two and three kaons, arehard to prepare and study experimentally. Here we show how to extract thisinformation using first-principle lattice QCD results. We (1) extend therelativistic three-body quantization condition to the strangeness sector,predicting for the first time the excited level finite-volume spectrum of threekaon systems at maximal isospin, and (2) present a first lattice QCDcalculation of the excited levels of this system in a finite box. We compareour predictions with the lattice results reported here and with previous groundstate calculations and find very good agreement.

Finite-volume energy spectrum of the $K^-K^-K^-$ system