  We study the boundary contribution to the low energy effective action of the
open string describing the confining flux tube in gauge theories. The form of
the boundary terms is strongly constrained by the requirement of Lorentz
symmetry, which is spontaneously broken by the formation of a long confining
flux tube in the vacuum. Writing the boundary action as an expansion in the
derivatives of the Nambu-Goldstone modes describing the transverse fluctuations
of the string, we single out and put in a closed form the first few Lorentz
invariant boundary terms. We also evaluate the leading deviation from the
Nambu-Goto string produced by the boundary action on the vacuum expectation
value of the Wilson loop and we test this prediction in the 3d Ising gauge
model. Our simulation attains a level of precision which is sufficient to test
the contribution of this term.
