Correlation Functions in $\textrm{T}\bar{\textrm{T}}$-deformed Theories on the Torus
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arXiv
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| Format: | Preprint |
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2024
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| author | Barel, Netanel |
| author_facet | Barel, Netanel |
| contents | We study the correlation functions of local operators in unitary $\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a torus, using their formulation in terms of Jackiw-Teitelboim gravity. We focus on the two-point correlation function in momentum space when the undeformed theory is a conformal field theory. The large momentum behavior of the correlation function is computed and compared to that of $\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a plane. For the latter, the behavior found was $\left(\frac{\sqrt{t}|q|}{πe}\right)^{-\frac{tq^2}π}$, 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: $\left(\frac{2\sqrt{t}^5q^2}{πe L^3|T|^2}\right)^{\frac{tq^2}π}$, where $T$ is the modular parameter 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15090 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Correlation Functions in $\textrm{T}\bar{\textrm{T}}$-deformed Theories on the Torus Barel, Netanel High Energy Physics - Theory We study the correlation functions of local operators in unitary $\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a torus, using their formulation in terms of Jackiw-Teitelboim gravity. We focus on the two-point correlation function in momentum space when the undeformed theory is a conformal field theory. The large momentum behavior of the correlation function is computed and compared to that of $\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a plane. For the latter, the behavior found was $\left(\frac{\sqrt{t}|q|}{πe}\right)^{-\frac{tq^2}π}$, 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: $\left(\frac{2\sqrt{t}^5q^2}{πe L^3|T|^2}\right)^{\frac{tq^2}π}$, where $T$ is the modular parameter 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. |
| title | Correlation Functions in $\textrm{T}\bar{\textrm{T}}$-deformed Theories on the Torus |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.15090 |