Generalized Free Conformal Field Theories at Infinite Temperature -- In memory of Iwasaki-sensei

Can space-time symmetries such as Lorentz, dilatation, or conformal symmetry be recovered at infinite temperature? To address this question, we study correlation functions of generalized free conformal field theories (a.k.a free holographic theories in thermal AdS space-time) at infinite temperature. We show that they are broken at the leading order in bosonic correlation functions, but a non-trivial scaling symmetry may emerge.