Correlation functions in T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed theories on the torus
Abstract We study the correlation functions of local operators in unitary T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed field theories defined on a torus, using their formulation in terms of Jackiw-Teitelboim gravity. We focus on the two-point correlation functions in momentum space when the...
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2024-11-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP11(2024)167 |
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| author | Netanel Barel |
| author_facet | Netanel Barel |
| author_sort | Netanel Barel |
| collection | DOAJ |
| description | Abstract We study the correlation functions of local operators in unitary T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed field theories defined on a torus, using their formulation in terms of Jackiw-Teitelboim gravity. We focus on the two-point correlation functions in momentum space when the undeformed theory is a conformal field theory. The large momentum behavior of the correlation functions is computed and compared to that of T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed field theories defined on a plane. For the latter, the behavior found was t q πe − tq 2 π $$ {\left(\frac{\sqrt{t}\left|q\right|}{\pi e}\right)}^{-\frac{tq^2}{\pi }} $$ , where q is the momentum and t is the deformation parameter. For a torus, the same behavior is found for |q| ≪ L/t, where L is the torus’ length scale. However, for |q| ≫ L/t, a different behavior is found: 2 t 5 q 2 πe L 3 T 2 tq 2 π $$ {\left(\frac{2{\sqrt{t}}^5{q}^2}{\pi e{L}^3{\left|T\right|}^2}\right)}^{\frac{tq^2}{\pi }} $$ , where T is the complex structure of the torus. Hence, at large momentum, the correlator decays and then grows. This behavior suggests that operators carrying momentum q are smeared on a distance scale t|q|. The difference from the plane’s result illustrates the non-locality of the theory and the UV-IR mixing. |
| format | Article |
| id | doaj-art-a4e6f194f6b645c3b220386b24373c83 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-a4e6f194f6b645c3b220386b24373c832024-12-08T12:09:09ZengSpringerOpenJournal of High Energy Physics1029-84792024-11-0120241114610.1007/JHEP11(2024)167Correlation functions in T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed theories on the torusNetanel Barel0Department of Particle Physics and Astrophysics, Weizmann Institute of ScienceAbstract We study the correlation functions of local operators in unitary T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed field theories defined on a torus, using their formulation in terms of Jackiw-Teitelboim gravity. We focus on the two-point correlation functions in momentum space when the undeformed theory is a conformal field theory. The large momentum behavior of the correlation functions is computed and compared to that of T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed field theories defined on a plane. For the latter, the behavior found was t q πe − tq 2 π $$ {\left(\frac{\sqrt{t}\left|q\right|}{\pi e}\right)}^{-\frac{tq^2}{\pi }} $$ , where q is the momentum and t is the deformation parameter. For a torus, the same behavior is found for |q| ≪ L/t, where L is the torus’ length scale. However, for |q| ≫ L/t, a different behavior is found: 2 t 5 q 2 πe L 3 T 2 tq 2 π $$ {\left(\frac{2{\sqrt{t}}^5{q}^2}{\pi e{L}^3{\left|T\right|}^2}\right)}^{\frac{tq^2}{\pi }} $$ , where T is the complex structure of the torus. Hence, at large momentum, the correlator decays and then grows. This behavior suggests that operators carrying momentum q are smeared on a distance scale t|q|. The difference from the plane’s result illustrates the non-locality of the theory and the UV-IR mixing.https://doi.org/10.1007/JHEP11(2024)167Field Theories in Lower DimensionsRenormalization and Regularization |
| spellingShingle | Netanel Barel Correlation functions in T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed theories on the torus Journal of High Energy Physics Field Theories in Lower Dimensions Renormalization and Regularization |
| title | Correlation functions in T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed theories on the torus |
| title_full | Correlation functions in T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed theories on the torus |
| title_fullStr | Correlation functions in T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed theories on the torus |
| title_full_unstemmed | Correlation functions in T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed theories on the torus |
| title_short | Correlation functions in T T ¯ $$ \textrm{T}\overline{\textrm{T}} $$ -deformed theories on the torus |
| title_sort | correlation functions in t t ¯ textrm t overline textrm t deformed theories on the torus |
| topic | Field Theories in Lower Dimensions Renormalization and Regularization |
| url | https://doi.org/10.1007/JHEP11(2024)167 |
| work_keys_str_mv | AT netanelbarel correlationfunctionsintttextrmtoverlinetextrmtdeformedtheoriesonthetorus |