Beschreibung:
<jats:title>A<jats:sc>bstract</jats:sc>
</jats:title><jats:p>We show that method of characteristics provides a powerful new point of view on <jats:inline-formula><jats:alternatives><jats:tex-math>$$ T\overline{T} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>T</mml:mi>
<mml:mover>
<mml:mi>T</mml:mi>
<mml:mo>¯</mml:mo>
</mml:mover>
</mml:math></jats:alternatives></jats:inline-formula>-and related deformations. Previously, the method of characteristics has been applied to <jats:inline-formula><jats:alternatives><jats:tex-math>$$ T\overline{T} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>T</mml:mi>
<mml:mover>
<mml:mi>T</mml:mi>
<mml:mo>¯</mml:mo>
</mml:mover>
</mml:math></jats:alternatives></jats:inline-formula>-deformation mainly to solve Burgers’ equation, which governs the deformation of the <jats:italic>quantum</jats:italic> spectrum. In the current work, we study <jats:italic>classical</jats:italic> deformed quantities using this method and show that <jats:inline-formula><jats:alternatives><jats:tex-math>$$ T\overline{T} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>T</mml:mi>
<mml:mover>
<mml:mi>T</mml:mi>
<mml:mo>¯</mml:mo>
</mml:mover>
</mml:math></jats:alternatives></jats:inline-formula> flow can be seen as a characteristic flow. Exploiting this point of view, we re-derive a number of important known results and obtain interesting new ones. We prove the equivalence between dynamical change of coordinates and the generalized light-cone gauge approaches to <jats:inline-formula><jats:alternatives><jats:tex-math>$$ T\overline{T} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>T</mml:mi>
<mml:mover>
<mml:mi>T</mml:mi>
<mml:mo>¯</mml:mo>
</mml:mover>
</mml:math></jats:alternatives></jats:inline-formula>-deformation. We find the deformed Lagrangians for a class of <jats:inline-formula><jats:alternatives><jats:tex-math>$$ T\overline{T} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>T</mml:mi>
<mml:mover>
<mml:mi>T</mml:mi>
<mml:mo>¯</mml:mo>
</mml:mover>
</mml:math></jats:alternatives></jats:inline-formula>-like deformations in higher dimensions and the (<jats:inline-formula><jats:alternatives><jats:tex-math>$$ T\overline{T} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>T</mml:mi>
<mml:mover>
<mml:mi>T</mml:mi>
<mml:mo>¯</mml:mo>
</mml:mover>
</mml:math></jats:alternatives></jats:inline-formula>)<jats:sup><jats:italic>α</jats:italic></jats:sup>-deformation in 2d with generic <jats:italic>α</jats:italic>, generalizing recent results in [1] and [2].</jats:p>