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

Abstract

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.