It is shown that the finite size corrections to the spectrum of the giant
magnon solution of classical string theory, computed using the uniform
light-cone gauge, are gauge invariant and have physical meaning. This is seen
in two ways: from a general argument where the single magnon is made gauge
invariant by putting it on an orbifold as a wrapped state obeying the level
matching condition as well as all other constraints, and by an explicit
calculation where it is shown that physical quantum numbers do not depend on
the uniform light-cone gauge parameter. The resulting finite size effects are
exponentially small in the R-charge and the exponent (but not the prefactor)
agrees with gauge theory computations using the integrable Hubbard model.Comment: 12 pages, some clarifications, references adde