We generalise Merzlyakov's theorem about the first-order theory of non-abelian free groups to all acylindrically hyperbolic groups. As a corollary, we deduce that if $G$ is an group and $E(G)$ denotes unique maximal finite normal subgroup $G$, then HNN extension $G\dot{\ast}_{E(G)}$, which simply product $G\ast\mathbb{Z}$ when trivial, have same $\forall\exists$-theory. consequence, prove follo...

Spectra with full towers of levels are expected due to the quantization string vibrations, however different theoretical models exist for excitation spectra. First principle computations important test and search novel phenomena, but so far only a few excited states QCD flux tubes have been studied pure gauge SU(3) lattice in 3+1 dimensions. We thus aim study spectrum static quark antiquark sou...