Tauberian-Cardy formula with spin
Abstract We prove a 2 dimensional Tauberian theorem in context of 2 dimensional conformal field theory. The asymptotic density of states with conformal weight (h, h ¯ $$ \overline{h} $$ ) → (∞, ∞) for any arbitrary spin is derived using the theorem. We further rigorously show that the error term is...
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)135 |
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| author | Sridip Pal Zhengdi Sun |
| author_facet | Sridip Pal Zhengdi Sun |
| author_sort | Sridip Pal |
| collection | DOAJ |
| description | Abstract We prove a 2 dimensional Tauberian theorem in context of 2 dimensional conformal field theory. The asymptotic density of states with conformal weight (h, h ¯ $$ \overline{h} $$ ) → (∞, ∞) for any arbitrary spin is derived using the theorem. We further rigorously show that the error term is controlled by the twist parameter and insensitive to spin. The sensitivity of the leading piece towards spin is discussed. We identify a universal piece in microcanonical entropy when the averaging window is large. An asymptotic spectral gap on (h, h ¯ $$ \overline{h} $$ ) plane, hence the asymptotic twist gap is derived. We prove an universal inequality stating that in a compact unitary 2D CFT without any conserved current Ag ≤ π c − 1 r 2 24 $$ Ag\le \frac{\pi \left(c-1\right){r}^2}{24} $$ is satisfied, where g is the twist gap over vacuum and A is the minimal “areal gap”, generalizing the minimal gap in dimension to (h′, h ¯ ′ $$ \overline{h}^{\prime } $$ ) plane and r = 4 3 π ≃ 2.21 $$ r=\frac{4\sqrt{3}}{\pi}\simeq 2.21 $$ . We investigate density of states in the regime where spin is parametrically larger than twist with both going to infinity. Moreover, the large central charge regime is studied. We also probe finite twist, large spin behavior of density of states. |
| format | Article |
| id | doaj-art-2cc3c88efb2845078c5232dfecbaa2bc |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-2cc3c88efb2845078c5232dfecbaa2bc2025-01-26T12:11:37ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020115410.1007/JHEP01(2020)135Tauberian-Cardy formula with spinSridip Pal0Zhengdi Sun1Department of Physics, University of California San DiegoDepartment of Physics, University of California San DiegoAbstract We prove a 2 dimensional Tauberian theorem in context of 2 dimensional conformal field theory. The asymptotic density of states with conformal weight (h, h ¯ $$ \overline{h} $$ ) → (∞, ∞) for any arbitrary spin is derived using the theorem. We further rigorously show that the error term is controlled by the twist parameter and insensitive to spin. The sensitivity of the leading piece towards spin is discussed. We identify a universal piece in microcanonical entropy when the averaging window is large. An asymptotic spectral gap on (h, h ¯ $$ \overline{h} $$ ) plane, hence the asymptotic twist gap is derived. We prove an universal inequality stating that in a compact unitary 2D CFT without any conserved current Ag ≤ π c − 1 r 2 24 $$ Ag\le \frac{\pi \left(c-1\right){r}^2}{24} $$ is satisfied, where g is the twist gap over vacuum and A is the minimal “areal gap”, generalizing the minimal gap in dimension to (h′, h ¯ ′ $$ \overline{h}^{\prime } $$ ) plane and r = 4 3 π ≃ 2.21 $$ r=\frac{4\sqrt{3}}{\pi}\simeq 2.21 $$ . We investigate density of states in the regime where spin is parametrically larger than twist with both going to infinity. Moreover, the large central charge regime is studied. We also probe finite twist, large spin behavior of density of states.https://doi.org/10.1007/JHEP01(2020)135Conformal and W SymmetryConformal Field Theory |
| spellingShingle | Sridip Pal Zhengdi Sun Tauberian-Cardy formula with spin Journal of High Energy Physics Conformal and W Symmetry Conformal Field Theory |
| title | Tauberian-Cardy formula with spin |
| title_full | Tauberian-Cardy formula with spin |
| title_fullStr | Tauberian-Cardy formula with spin |
| title_full_unstemmed | Tauberian-Cardy formula with spin |
| title_short | Tauberian-Cardy formula with spin |
| title_sort | tauberian cardy formula with spin |
| topic | Conformal and W Symmetry Conformal Field Theory |
| url | https://doi.org/10.1007/JHEP01(2020)135 |
| work_keys_str_mv | AT sridippal tauberiancardyformulawithspin AT zhengdisun tauberiancardyformulawithspin |