On the universal behavior of T T ¯ $$ T\overline{T} $$ -deformed CFTs: single and double-trace partition functions at large c
Abstract We study universal properties of the torus partition function of T T ¯ $$ T\overline{T} $$ -deformed CFTs under the assumption of modular invariance, for both the original version, referred to as the double-trace version in this paper, and the single-trace version defined as the symmetric p...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-05-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2023)210 |
| _version_ | 1827859797112782848 |
|---|---|
| author | Luis Apolo Wei Song Boyang Yu |
| author_facet | Luis Apolo Wei Song Boyang Yu |
| author_sort | Luis Apolo |
| collection | DOAJ |
| description | Abstract We study universal properties of the torus partition function of T T ¯ $$ T\overline{T} $$ -deformed CFTs under the assumption of modular invariance, for both the original version, referred to as the double-trace version in this paper, and the single-trace version defined as the symmetric product orbifold of double-trace T T ¯ $$ T\overline{T} $$ -deformed CFTs. In the double-trace case, we specify sparseness conditions for the light states for which the partition function at low temperatures is dominated by the vacuum when the central charge of the undeformed CFT is large. Using modular invariance, this implies a universal density of high energy states, in analogy with the behavior of holographic CFTs. For the single-trace T T ¯ $$ T\overline{T} $$ deformation, we show that modular invariance implies that the torus partition function can be written in terms of the untwisted partition function and its modular images, the latter of which can be obtained from the action of a generalized Hecke operator. The partition function and the energy of twisted states match holographic calculations in previous literature, thus providing further evidence for the conjectured holographic correspondence. In addition, we show that the single-trace partition function is universal when the central charge of the undeformed CFT is large, without needing to assume a sparse density of light states. Instead, the density of light states is shown to always saturate the sparseness condition. |
| first_indexed | 2024-03-12T13:13:42Z |
| format | Article |
| id | doaj.art-ae830a063c3f4dc99d934e70cc67f5bb |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T13:13:42Z |
| publishDate | 2023-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-ae830a063c3f4dc99d934e70cc67f5bb2023-08-27T11:06:06ZengSpringerOpenJournal of High Energy Physics1029-84792023-05-012023513010.1007/JHEP05(2023)210On the universal behavior of T T ¯ $$ T\overline{T} $$ -deformed CFTs: single and double-trace partition functions at large cLuis Apolo0Wei Song1Boyang Yu2Institute for Theoretical Physics, University of AmsterdamYau Mathematical Sciences Center, Tsinghua UniversityCenter for High Energy Physics, Peking UniversityAbstract We study universal properties of the torus partition function of T T ¯ $$ T\overline{T} $$ -deformed CFTs under the assumption of modular invariance, for both the original version, referred to as the double-trace version in this paper, and the single-trace version defined as the symmetric product orbifold of double-trace T T ¯ $$ T\overline{T} $$ -deformed CFTs. In the double-trace case, we specify sparseness conditions for the light states for which the partition function at low temperatures is dominated by the vacuum when the central charge of the undeformed CFT is large. Using modular invariance, this implies a universal density of high energy states, in analogy with the behavior of holographic CFTs. For the single-trace T T ¯ $$ T\overline{T} $$ deformation, we show that modular invariance implies that the torus partition function can be written in terms of the untwisted partition function and its modular images, the latter of which can be obtained from the action of a generalized Hecke operator. The partition function and the energy of twisted states match holographic calculations in previous literature, thus providing further evidence for the conjectured holographic correspondence. In addition, we show that the single-trace partition function is universal when the central charge of the undeformed CFT is large, without needing to assume a sparse density of light states. Instead, the density of light states is shown to always saturate the sparseness condition.https://doi.org/10.1007/JHEP05(2023)210AdS-CFT CorrespondenceField Theories in Lower DimensionsIntegrable Field TheoriesString Duality |
| spellingShingle | Luis Apolo Wei Song Boyang Yu On the universal behavior of T T ¯ $$ T\overline{T} $$ -deformed CFTs: single and double-trace partition functions at large c Journal of High Energy Physics AdS-CFT Correspondence Field Theories in Lower Dimensions Integrable Field Theories String Duality |
| title | On the universal behavior of T T ¯ $$ T\overline{T} $$ -deformed CFTs: single and double-trace partition functions at large c |
| title_full | On the universal behavior of T T ¯ $$ T\overline{T} $$ -deformed CFTs: single and double-trace partition functions at large c |
| title_fullStr | On the universal behavior of T T ¯ $$ T\overline{T} $$ -deformed CFTs: single and double-trace partition functions at large c |
| title_full_unstemmed | On the universal behavior of T T ¯ $$ T\overline{T} $$ -deformed CFTs: single and double-trace partition functions at large c |
| title_short | On the universal behavior of T T ¯ $$ T\overline{T} $$ -deformed CFTs: single and double-trace partition functions at large c |
| title_sort | on the universal behavior of t t ¯ t overline t deformed cfts single and double trace partition functions at large c |
| topic | AdS-CFT Correspondence Field Theories in Lower Dimensions Integrable Field Theories String Duality |
| url | https://doi.org/10.1007/JHEP05(2023)210 |
| work_keys_str_mv | AT luisapolo ontheuniversalbehavioroftttoverlinetdeformedcftssingleanddoubletracepartitionfunctionsatlargec AT weisong ontheuniversalbehavioroftttoverlinetdeformedcftssingleanddoubletracepartitionfunctionsatlargec AT boyangyu ontheuniversalbehavioroftttoverlinetdeformedcftssingleanddoubletracepartitionfunctionsatlargec |