Kaluza-Klein spectrometry for $\mathrm{A}\mathrm{d}{\mathrm{S}}_3$ vacua

We use exceptional field theory to compute Kaluza-Klein mass spectra around $\mathrm{A}\mathrm{d}{\mathrm{S}}_3$ vacua that sit in half-maximal gauged supergravity in three dimensions. The formalism applies to any vacuum that arises from a consistent truncation of higher-dimensional supergravity, no matter what symmetries are preserved. We illustrate its efficiency by computing the spectra of ${\cal N}=(2,0)$and${\cal N}=(1,1)$six-dimensionalsupergravitieson${\rm AdS_{3}}\times S^{3}$andoftypeIIsupergravityon${\rm AdS_{3}}\times S^{3}\times S^{3}\times S^{1}$.