Marginal TT over line -like deformation and modified Maxwell theories in two dimensions

Recently, the ModMax theory has been proposed as a unique conformal nonlinear extension of electrodynamic theories. We have shown in [H. Babaei-Aghbolagh et al., Phys. Lett. B 829, 137079 (2022).] that this modification can be reproduced by using a marginal TT over bar -like deformation from pure Maxwell theory. Further, it was shown that this deformation is solvable by applying a perturbative approach. In this paper, we will investigate a similar marginal TT over bar -like deformation for a general two-dimensional scalar field theory. It is shown that employing an irrelevant TT over bar operator on this marginal scalar theory will produce a generalized Nambu-Goto action of this scalar theory which is a Born-Infeld-like action in two dimensions. Using a similar prescription for a two-dimensional theory with multiple scalar fields, we show that the marginal TT over bar -like deformation yields a ModMax-like Lagrangian and then the irrelevant operator produces a generalized scalar ModMax action.