Ultra-Violet Behavior of Bosonic Quantum Membranes

We treat the action for a bosonic membrane as a sigma model, and then compute quantum corrections by integrating out higher membrane modes. As in string theory, where the equations of motion of Einstein’s theory emerges by setting β = 0, we find that, with certain assumptions, we can recover the equations of motion for the background fields, i.e. Rμν +(1/4)FμαβγμF αβγ ν = 0 and DFαβγ = 0. for the membrane case. Although the membrane theory is non-renormalizable on the world volume by power counting, the investigation of the ultra-violet behavior of membranes may give us insight into the supersymmetric case, where we hope to obtain higher order M-theory corrections to 11 dimensional supergravity.