Fluxbrane-like backgrounds obtained from flat space by a sequence of
T-dualities and shifts of polar coordinates (beta deformations) provide an
interesting class of exactly solvable string theories. We compute the one-loop
partition function for various such deformed spaces and study their spectrum of
D-branes. For rational values of the B-field these models are equivalent to Z_N
\times Z_N orbifolds with discrete torsion. We also obtain an interesting new
class of time-dependent backgrounds which resemble localized closed string
tachyon condensation.Comment: 26 pages, harvmac, v2: statements about tachyons corrected, v3: very
minor change