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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2505.02897 |
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| _version_ | 1866908350688526336 |
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| author | Pal, Sridip Qiao, Jiaxin van Rees, Balt C. |
| author_facet | Pal, Sridip Qiao, Jiaxin van Rees, Balt C. |
| contents | 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 $\exp\left( π\sqrt{\frac{2}{3}(c-1) J} \right)/\sqrt{2J}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02897 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality of the microcanonical entropy at large spin Pal, Sridip Qiao, Jiaxin van Rees, Balt C. High Energy Physics - Theory Statistical Mechanics Mathematical Physics 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 $\exp\left( π\sqrt{\frac{2}{3}(c-1) J} \right)/\sqrt{2J}$ 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. |
| title | Universality of the microcanonical entropy at large spin |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2505.02897 |