Brane world scenario with m-form field: stabilisation of radion modulus and self-tuning solutions

We consider (n+m+1)-dimensional bulk spacetime, containing flat (n+m−1)-dimensional parallel branes, with topology Rn−1×Tm. We assume that the graviton and an m-form field are the only bulk fields and that the m-form field has nonvanishing components along the Tm directions only. We then find that the m-form field, with suitable bulk and brane potentials, can stabilise the radion modulus at the required value with no fine tuning. We find self-tuning solutions also.