2025/05/05 by Pal, Sridip, Qiao, Jiaxin, van Rees, Balt C. · 2 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2505.02897
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( π√((2)/(3)(c-1) J) )/√(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.