Quantum vacuum effects for a massive Bosonic string in background B-field

We study the Casimir effect for a Bosonic string extended between D-branes, and living in a flat space with an antisymmetric background B-field. We find the Casimir energy as a function of the B-field, and the mass-parameter of the string, and accordingly we obtain a B-dependence correction term to the ground-state mass of the string. We show that for sufficiently large B-field, the ground state of the string contains real (i.e. non-Tachyonic) particles.