An interesting link between the effective string theory describing the colour confinement in Yang-Mills theories and conformal field theories perturbed by the composite operator $T \bar{T}$ was recently discovered. We will discuss various aspects of this special kind of integrable perturbation and how it affects the energy levels of a generic 2D Quantum Field Theory, through a surprising relation with the inviscid Burgers equation. As this class of models corresponds to non-Wilsonian RG trajectories, these studies may help to clarify important aspects concerning the appearance of singularities in effective QFT, and hopefully be useful in the effective string framework.