  In presence of a static pair of sources, the spectrum of low-lying states of
whatever confining gauge theory in D space-time dimensions is described, at
large source separations, by an effective string theory. In the far infrared
the latter flows, in the static gauge, to a two-dimensional massless free-field
theory. It is known that the Lorentz invariance of the gauge theory fixes
uniquely the first few subleading corrections of this free-field limit. We
point out that the first allowed correction - a quartic polynomial in the field
derivatives - is exactly the composite field $T\bar{T}$, built with the chiral
components, $T$ and $\bar{T}$, of the energy-momentum tensor. This irrelevant
perturbation is quantum integrable and yields, through the thermodynamic Bethe
Ansatz (TBA),the energy levels of the string which exactly coincide with the
Nambu-Goto spectrum. We obtain this way the results recently found by Dubovsky,
Flauger and Gorbenko. This procedure easily generalizes to any two-dimensional
CFT. It is known that the leading deviation of the Nambu-Goto spectrum comes
from the boundary terms of the string action. We solve the TBA equations on an
infinite strip, identify the relevant boundary parameter and verify that it
modifies the string spectrum as expected.
