Semi-universality of CFT$_d$ entropy at large spin

The thermal partition function, Z Z , of a CFT_d C F T d on S^{d-1} S d − 1 is parameterized by the inverse temperature \beta β along with \lfloor d/2\rfloor ⌊ d / 2 ⌋ angular velocities \omega_i ω i . In this paper, we investigate the behaviour of this partition function when n n of the \omega_i ω i are scaled to unity (the largest allowed value) at fixed values of the other (\lfloor d/2\rfloor-n) ( ⌊ d / 2 ⌋ − n ) angular velocities. We argue that \ln Z ln ⁡ Z develops a simple pole in (1-\omega_i) ( 1 − ω i ) for each \omega_i ω i that is scaled to unity. The residue of this product of poles is a theory-dependent (so non-universal) function of \beta β and the fixed angular velocities. The inverse Laplace transformation of this partition function constrains the functional form of the field theory entropy as a function of charges in a limit in which angular momenta and the twist are scaled as follows. While n n special angular momenta J_1\ldots J_n J 1 …