Bosonic Bogoliubov transformations as Lorentz boosts in (c,c¯)=(1,1) conformal field theories with marginal JJ¯ deformations

In this paper, we consider conformal field theories with central charges [Formula: see text] that are invariant under the exchange of the holomorphic and antiholomorphic sectors, in both bosonic and fermionic realizations that are meaningful for condensed matter systems. The effect of marginal current–current [Formula: see text] perturbations is to induce a deformation of the Hilbert space given by a Lorentz boost in the 2D space of currents, which is identified with a Bogoliubov transformation. The rapidity of the boost is determined by the coupling constant of the marginal perturbation. When the perturbation is diagonal in the original currents of the theory, there is a linear relation between the two, and nonlinear otherwise. In the fermionic cases, both free and with Calogero–Sutherland interactions, the marginal perturbation corresponds to backward scattering processes.