A universal sector of $\mathcal{N}=1$ class $\mathcal{S}$ spectra

We determine a universal sector of the spectrum of light operators in four-dimensional $\mathcal{N}=1$ class $\mathcal{S}$ superconformal field theories arising from M5-branes wrapped on a compact hyperbolic Riemann surface ${\mathrm{\Sigma }}_2$. We work at large $N$, analysing Kaluza–Klein fluctuations about the dual Bah–Beem–Bobev–Wecht anti-de Sitter backgrounds for general values of the twist parameter $z$. To obtain these spectra, we specialise recently derived mass operators to modes that are constant on ${\mathrm{\Sigma }}_2$ by imposing a suitable $z$-dependent generalised $G$-structure. We then organise the resulting eigenstates into long and protected $\mathcal{N}=1$ supermultiplets with definite flavour quantum numbers. As $z$ varies, rich patterns emerge in the spectrum, including both isolated multiplets and infinite towers of multiplets, which we characterise analytically.