Vacuum structure of Toroidal Carbon Nanotubes

Low energy excitations in carbon nanotubes can be described by an effective field theory of two components spinor. It is pointed out that the chiral anomaly in 1+1 dimensions should be observed in a metallic toroidal carbon nanotube on a planar geometry with varying magnetic field. We propose an experimental setup for studying this quantum effect. We also analyze the vacuum structure of the metallic toroidal carbon nanotube including the Coulomb interactions and discuss some effects of external charges on the vacuum.