Hawking--Page Universality, Thermodynamic Dipoles and Categorical Defects (opens in new tab)

We reconsider the Hawking--Page transition using the common thermodynamic vector field whose zeros include the Davies and Hawking--Page points. In the elementary AdS branch their winding numbers are $w_{\rm D}=-1$ and $w_{\rm HP}=+1$, so the pair has zero total charge but a non-zero signed first moment. After normalization by the Davies scales this moment gives the familiar universal ratios $C_S$ and $C_T$; in four dimensions $C_S=2$ and $C_T=...