TTbar deformation of Calogero-Sutherland model via dimensional reduction

The significant progress in studying TTbar relativistic quantum field theories has motivated the recent formulation of TTbar-like deformations for the more general case of non-Lorentz invariant QFTs as well as integrable many-body systems. On the example of free particles and the Calogero-Sutherland model, we describe a new TTbar-like deformation of non-relativistic many-body quantum mechanics. First, we perform the dynamical change of coordinates to derive a generalization of the "trace relation" and apply it to the non-linear Schrodinger model. After that, we work out the dimensional reduction of the bilinear TTbar operator and obtain the new T Tbar-like deformation. The deformation modifies the spectrum of the Hamiltonian but does not alter its eigenfunctions. The deformed classical Lagrangian is also obtained. Finally, we study a particular deformation of the two-dimensional Yang-Mills theory that maps the gauge theory onto a system of TT-perturbed fermions.