Geodesic
$T\overline T$ deformation of Calogero-Sutherland model via dimensional reduction
Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 358-377

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We derive a general expression for the trace of the energy-momentum tensor $T\overline T$-deformed field theories using a dynamical change of coordinates. Then we perform a dimensional reduction of the bilinear $T\overline T$ operator and obtain a new $T\overline T$-like deformation of the quantum mechanics of free nonrelativistic fermions and the interacting Calogero-Sutherland system. The deformation leads to a change in the energy spectrum but does not affect the eigenfunctions. Furthermore, an expression for the deformed classical Lagrangian is obtained. We also study the correspondence between the two-dimensional Yang-Mills theory and the Calogero-Sutherland system in the presence of the deformation.
Keywords: Field Theories in Lower Dimensions, Integrability, Quantum Mechanics. 
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     author = {D. V. Pavshinkin},
     title = {$T\overline T$ deformation of {Calogero-Sutherland} model via dimensional reduction},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {358--377},
     publisher = {mathdoc},
     volume = {217},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a7/}
}
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D. V. Pavshinkin. $T\overline T$ deformation of Calogero-Sutherland model via dimensional reduction. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 358-377. http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a7/