Two-dimensional field theories deformed by Zamolodchikov's TTbar operator have recently attracted the attention of theoretical physicists due to the many important links with string theory and AdS/CFT. In this talk, I will describe various classical and quantum aspects of this particular irrelevant perturbation, including its geometrical interpretation at the classical level. I will also introduce a generalisation of this geometrical framework to 4D field theories, and discuss some of the interesting differences with the 2D case. ---- Part of London Integrability Journal Club. If you are a new participant, please register filling the form at integrability-london.weebly.com. The link will be emailed.

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.