$T\overline T$ Deformation and the Light-Cone Gauge

The homogeneous inviscid Burgers equation, which determines the spectrum of a $T\overline T$ deformed model, has a natural interpretation as the condition of the gauge invariance of the target space–time energy and momentum of a (non-critical) string theory quantised in a generalised uniform light-cone gauge which depends on the deformation parameter. As a simple application of the light-cone gauge interpretation, we derive the $T\overline T$ deformed Lagrangian for a system of any number of scalars, fermions and chiral bosons with an arbitrary potential. We find that the $T\overline T$ deformation is driven by the canonical Noether stress–energy tensor but not the covariant one.