Magnetic backgrounds and tachyonic instabilities in closed superstring theory and M-theory

Models of closed superstrings in certain curved NS-NS magnetic flux backgrounds are exactly solvable in terms of free fields. They interpolate between free superstring theories with periodic and antiperiodic boundary conditions for fermions around some compact direction, and, in particular, between type 0 and type II string theories. Using ``9-11 flip'', this interpolation can be extended to M-theory and provides an interesting setting for a study of tachyon problem in closed string theory. Starting with a general 2-parameter family of such Melvin-type models, we present several new magnetic flux backgrounds in 10-d string theory and 11-d M-theory and discuss their tachyonic instabilities. In particular, we suggest a description of type 0B theory in terms of M-theory in curved magnetic flux background, which supports its conjectured SL(2,Z) symmetry, and in which the type 0 tachyon appears to correspond to a state in 11-d supergravity multiplet. In another ``T-dual'' description, the tachyon is related to a winding membrane state.