  We study continuously self-similar solutions of four-dimensional
Einstein-Maxwell-dilaton theory, with an arbitrary dilaton coupling.
Self-similarity is an emergent symmetry of gravitational collapse near the
threshold of black hole formation. The resulting `critical collapse' picture
has been intensively studied in the past for self-gravitating scalar fields or
perfect fluids, but little is known concerning other systems. Here we assess
the impact of gauge fields on critical collapse, in the context of low-energy
string theories. Matter fields need not inherit the symmetries of a spacetime.
We determine the homothetic conditions that scale-invariance of the metric
imposes on the dilaton and electromagnetic fields, and we obtain their general
solution. The inclusion of a potential for the dilaton is compatible with the
homothetic conditions if and only if it is of the Liouville type. By imposing
also spherical symmetry, a detailed analysis of critical collapse in these
systems is possible by casting the field equations as an autonomous system. We
find analytically that Choptuik's critical exponent depends on the dilaton
coupling. Despite this and the presence of two novel fixed points, the
electromagnetic field necessarily vanishes for the critical solution.
