  We present the results of a new search for variable stars in the Local Group
dwarf galaxy Leo A, based on deep photometry from the Advanced Camera for
Surveys onboard the Hubble Space Telescope. We detected 166 bona fide variables
in our field, of which about 60 percent are new discoveries, and 33 candidate
variables. Of the confirmed variables, we found 156 Cepheids, but only 10 RR
Lyrae stars despite nearly 100 percent completeness at the magnitude of the
horizontal branch. The RR Lyrae stars include 7 fundamental and 3
first-overtone pulsators, with mean periods of 0.636 and 0.366 day,
respectively. From their position on the period-luminosity (PL) diagram and
light-curve morphology, we classify 91, 58, and 4 Cepheids as fundamental,
first-overtone, and second-overtone mode Classical Cepheids (CC), respectively,
and two as population II Cepheids. However, due to the low metallicity of Leo
A, about 90 percent of the detected Cepheids have periods shorter than 1.5
days. Comparison with theoretical models indicate that some of the fainter
stars classified as CC could be Anomalous Cepheids. We estimate the distance to
Leo A using the tip of the RGB (TRGB) and various methods based on the
photometric and pulsational properties of the Cepheids and RR Lyrae stars. The
distances obtained with the TRGB and RR Lyrae stars agree well with each other
while that from the Cepheid PL relations is somewhat larger, which may indicate
a mild metallicity effect on the luminosity of the short-period Cepheids. Due
to its very low metallicity, Leo A thus serves as a valuable calibrator of the
metallicity dependencies of the variable star luminosities.
