$$T\overline T$$ deformation of the Calogero–Sutherland model via dimensional reduction

Abstract

We derive a general expression for the trace of the energy–momentum tensor $$T \kern0.9pt\overline{\vphantom{T}\kern6.0pt}\kern-6.9pt T $$ -deformed field theories using a dynamical change of coordinates. Then we perform a dimensional reduction of the bilinear $$T \kern0.9pt\overline{\vphantom{T}\kern6.0pt}\kern-6.9pt T $$ operator and obtain a new $$T \kern0.9pt\overline{\vphantom{T}\kern6.0pt}\kern-6.9pt T $$ -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.