$T\bar{T}$ deformation of Calogero-Sutherland model via dimensional reduction

Abstract

We perform the dynamical change of coordinates to derive a generalization of the trace relation and apply it to the non-linear Schrödinger model. After that, we work out the dimensional reduction of the bilinear $T\bar{T}$ operator and obtain the new $T\bar{T}$-like deformation of the quantum mechanics of free non-relativistic fermions and interacting Calogero-Sutherland particles. 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 $T\bar{T}$-perturbed fermions.

arXiv comment10 pages, 1 figure; v4

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