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In presence of a static pair of sources, the spectrum of low-lying states ofany confining gauge theory in D space-time dimensions is described, at largesource separations, by an effective string theory. Recently two importantadvances improved our understanding of this effective theory. First, it wasrealized that the form of the effective action is strongly constrained by therequirement of the Lorentz invariance of the gauge theory, which isspontaneously broken by the formation of a long confining flux tube in thevacuum. This constraint is strong enough to fix uniquely the first fewsubleading terms of the action. Second, it has been realized that the first ofthese allowed terms - a quartic polynomial in the field derivatives - isexactly the composite field $T\bar{T}$, built with the chiral components, $T$and $\bar{T}$, of the energy-momentum tensor of the 2d QFT describing theinfrared limit of the effective string. This irrelevant perturbation is quantumintegrable and yields, through the thermodynamic Bethe Ansatz (TBA), the energylevels of the string which exactly coincide with the Nambu-Goto spectrum. Inthis talk we first review the general implications of these two results andthen, as a test of the power of these methods, use them to construct the firstfew boundary corrections to the effective string action.

Recent progress in the effective string theory description of LGTs