Correlation functions in $$ \textrm{T}\overline{\textrm{T}} $$-deformed theories on the torus
Year: 2024
Type: article
Abstract: A bstract We study the correlation functions of local operators in unitary $$ \textrm{T}\overline{\textrm{T}} $$ T 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 $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ -deformed field theories defined on a plane. For the latter, the behavior found was $$ {\left(\frac{\sqrt{t}\left|q\right|}{\pi e}\right)}^{-\frac{tq^2}{\pi }} $$ t q πe − 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: $$ {\left(\frac{2{\sqrt{t}}^5{q}^2}{\pi e{L}^3{\left|T\right|}^2}\right)}^{\frac{tq^2}{\pi }} $$ 2 t 5 q 2 πe L 3 T 2 tq 2 π , 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.
Source: Journal of High Energy Physics
Author: Netanel Barel
Institution: Weizmann Institute of Science
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Award: G6786139606
OpenAlex ID: W4404959823