Work

Universality of the Microcanonical Entropy at Large Spin

Year: 2025

Type: article

Abstract: We consider rigorous consequences of modular invariance for two-dimensional unitary non-rational CFTs with $$c > 1$$ 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 $$\exp \left( \pi \sqrt{\frac{2}{3}(c-1) J} \right) /\sqrt{2J}$$ exp π 2 3 ( c - 1 ) J / 2 J in any twist interval at or above $$(c-1)/12$$ ( 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 $$(c-1)/12$$ ( 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.

Source: Communications in Mathematical Physics

DOI: 10.1007/s00220-025-05442-y

Authors: Sridip Pal, Jiaxin Qiao, Balt C. van Rees