A universal inequality on the unitary 2D CFT partition function
Abstract We prove the conjecture proposed by Hartman, Keller and Stoica (HKS) [1]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension c 12 $$ \frac{c}{12} $$ + ϵ and below the twist c 12 $$ \frac{c}{12} $$ is universal in the large c limit for all...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-07-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2025)163 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849238207070208000 |
|---|---|
| author | Indranil Dey Sridip Pal Jiaxin Qiao |
| author_facet | Indranil Dey Sridip Pal Jiaxin Qiao |
| author_sort | Indranil Dey |
| collection | DOAJ |
| description | Abstract We prove the conjecture proposed by Hartman, Keller and Stoica (HKS) [1]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension c 12 $$ \frac{c}{12} $$ + ϵ and below the twist c 12 $$ \frac{c}{12} $$ is universal in the large c limit for all β L β R ≠ 4π 2. The technique of the proof allows us to derive a one-parameter (with parameter α ∈ (0, 1]) family of universal inequalities on the unitary 2D CFT partition function with general central charge c ⩾ 0, using analytical modular bootstrap. We derive an iterative equation for the domain of validity of the inequality on the (β L , β R ) plane. The infinite iteration of this equation gives the boundary of maximal-validity domain, which depends on the parameter α in the inequality. In the c → ∞ limit, with the additional assumption of a sparse spectrum below the scaling dimension c 12 $$ \frac{c}{12} $$ + ϵ and the twist αc 12 $$ \frac{\alpha c}{12} $$ (with α ∈ (0, 1] fixed), our inequality shows that the grand-canonical free energy exhibits a universal large c behavior in the maximal-validity domain. This domain, however, does not cover the entire (β L , β R ) plane, except in the case of α = 1. For α = 1, this proves the conjecture proposed by HKS [1], and for α < 1, it quantifies how sparseness in twist affects the regime of universality. Furthermore, this implies a precise lower bound on the temperature of near-extremal BTZ black holes, above which we can trust the black hole thermodynamics. |
| format | Article |
| id | doaj-art-2a8e4c6ce78549cbb50d7c0310311d76 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-2a8e4c6ce78549cbb50d7c0310311d762025-08-20T04:01:42ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025714310.1007/JHEP07(2025)163A universal inequality on the unitary 2D CFT partition functionIndranil Dey0Sridip Pal1Jiaxin Qiao2Department of Theoretical Physics, Tata Institute of Fundamental ResearchWalter Burke Institute for Theoretical Physics, California Institute of TechnologyLaboratory for Theoretical Fundamental Physics, Institute of Physics, École Polytechnique Fédérale de LausanneAbstract We prove the conjecture proposed by Hartman, Keller and Stoica (HKS) [1]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension c 12 $$ \frac{c}{12} $$ + ϵ and below the twist c 12 $$ \frac{c}{12} $$ is universal in the large c limit for all β L β R ≠ 4π 2. The technique of the proof allows us to derive a one-parameter (with parameter α ∈ (0, 1]) family of universal inequalities on the unitary 2D CFT partition function with general central charge c ⩾ 0, using analytical modular bootstrap. We derive an iterative equation for the domain of validity of the inequality on the (β L , β R ) plane. The infinite iteration of this equation gives the boundary of maximal-validity domain, which depends on the parameter α in the inequality. In the c → ∞ limit, with the additional assumption of a sparse spectrum below the scaling dimension c 12 $$ \frac{c}{12} $$ + ϵ and the twist αc 12 $$ \frac{\alpha c}{12} $$ (with α ∈ (0, 1] fixed), our inequality shows that the grand-canonical free energy exhibits a universal large c behavior in the maximal-validity domain. This domain, however, does not cover the entire (β L , β R ) plane, except in the case of α = 1. For α = 1, this proves the conjecture proposed by HKS [1], and for α < 1, it quantifies how sparseness in twist affects the regime of universality. Furthermore, this implies a precise lower bound on the temperature of near-extremal BTZ black holes, above which we can trust the black hole thermodynamics.https://doi.org/10.1007/JHEP07(2025)163Conformal and W SymmetryField Theories in Lower DimensionsAdS-CFT CorrespondenceBlack Holes |
| spellingShingle | Indranil Dey Sridip Pal Jiaxin Qiao A universal inequality on the unitary 2D CFT partition function Journal of High Energy Physics Conformal and W Symmetry Field Theories in Lower Dimensions AdS-CFT Correspondence Black Holes |
| title | A universal inequality on the unitary 2D CFT partition function |
| title_full | A universal inequality on the unitary 2D CFT partition function |
| title_fullStr | A universal inequality on the unitary 2D CFT partition function |
| title_full_unstemmed | A universal inequality on the unitary 2D CFT partition function |
| title_short | A universal inequality on the unitary 2D CFT partition function |
| title_sort | universal inequality on the unitary 2d cft partition function |
| topic | Conformal and W Symmetry Field Theories in Lower Dimensions AdS-CFT Correspondence Black Holes |
| url | https://doi.org/10.1007/JHEP07(2025)163 |
| work_keys_str_mv | AT indranildey auniversalinequalityontheunitary2dcftpartitionfunction AT sridippal auniversalinequalityontheunitary2dcftpartitionfunction AT jiaxinqiao auniversalinequalityontheunitary2dcftpartitionfunction AT indranildey universalinequalityontheunitary2dcftpartitionfunction AT sridippal universalinequalityontheunitary2dcftpartitionfunction AT jiaxinqiao universalinequalityontheunitary2dcftpartitionfunction |