Universal pole conjecture for rotating conformal field theories

Determine whether the thermal free energies of all conformal field theories on a sphere develop a pole as the angular velocity approaches the inverse radius of the sphere, specifically at \(\hat\mu^2 r^2=1\).

Background

The paper situates its analysis within a conjecture that thermal free energies of conformal field theories with angular potential develop a pole when the angular velocity reaches the speed-of-light value in units of the sphere radius. The existence of such a pole is established in two dimensions using modular invariance and argued in higher dimensions using thermal effective field theory, but the statement is presented as a conjecture for conformal field theories generally.

The authors provide evidence for this conjecture by explicitly analyzing the large-$N$ critical $O(N)$ vector model on $S^1\times S^2$, showing that its leading high-temperature free energy has the predicted pole. Their calculation therefore addresses a nontrivial example but does not establish the conjecture for all conformal field theories.