Article Dans Une Revue Communications in Mathematical Physics Année : 2025

Universality of the microcanonical entropy at large spin

Sridip Pal
  • Fonction : Auteur
Jiaxin Qiao
  • Fonction : Auteur

Résumé

We consider rigorous consequences of modular invariance for two-dimensional unitary non-rational CFTs with $c > 1$. Simple estimates for the torus partition function can lead to remarkably strong results. We show in particular that the spectral density of spin-$J$ operators must grow like $\exp\left( \pi \sqrt{\frac{2}{3}(c-1) J} \right)/\sqrt{2J}$ in any twist interval at or above $(c-1)/12$, with a known twist-dependent prefactor. This proves that the large $J$ spectrum becomes dense even without averaging over spins. For twists below $(c-1)/12$ we establish that the growth must be strictly slower. Finally, we estimate how fast the maximal gap between two spin-$J$ operators must go to zero as $J$ becomes large.

Dates et versions

hal-05077848 , version 1 (21-05-2025)

Identifiants

Citer

Sridip Pal, Jiaxin Qiao, Balt C van Rees. Universality of the microcanonical entropy at large spin. Communications in Mathematical Physics, 2025, 406 (12), pp.302. ⟨10.1007/s00220-025-05442-y⟩. ⟨hal-05077848⟩
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