BOKS 45906: a CV with an orbital period of 56.6 min in the Kepler field?

BOKS 45906 was found to be a blue source in the Burrell-Optical-Kepler-Survey which showed a 3 mag outburst lasting ~5 d. We present the Kepler light curve of this source which covers nearly 3 years. We find that it is in a faint optical state for approximately half the time and shows a series of outbursts separated by distinct dips in flux. Using data with 1 min sampling, we find clear evidence that in its low state BOKS 45906 shows a flux variability on a period of 56.5574+/-0.0014 min and a semi-amplitude of ~3 percent. Since we can phase all the 1 min cadence data on a common ephemeris using this period, it is probable that 56.56 min is the binary orbital period. Optical spectra of BOKS 45906 show the presence of Balmer lines in emission indicating it is not an AM CVn (pure Helium) binary. Swift data show that it is a weak X-ray source and is weakly detected in the bluest of the UVOT filters. We conclude that BOKS 45906 is a cataclysmic variable with a period shorter than the `period-bounce' systems and therefore BOKS 45906 could be the first helium-rich cataclysmic variable detected in the Kepler field.