Аннотация:

We consider the deformation of two-dimensional field theories by the TT-bar operator. This operator for 2-dimensional theories can be represented as the determinant of the stress-energy tensor of the original theory. It is shown that the TT-bar deformation of the 2D free scalar field theory leads to the bosonic string Lagrangian in static gauge in 3d spacetime. The simplest case of the Toda chain for two particles is considered. Using the representation in terms of Lax pairs, the integrability of this model is shown. The TT-bar deformation for a generalisation of this model to the Toda field theory is obtained (the Sinh-Gordon model). The reduction of the 5-dimensional model of a truncated supergravity with scalar and electromagnetic fields is performed to an integrable mechanical model, using the cosmological ansatz for the metric and under the assumption that the fields depend only on time.