Equivalence of massless boson and fermion theories in curved two-dimensional space-time: Sugawara stress tensor

Abstract

It is shown that the well known equivalence of two-dimensional massless scalar and spinor quantum field theories extends to curved space-time. The vacuum Sugawara stress tensor for a spinor field is evaluated by a covariant point-separation procedure and found to be identical to the scalar vacuum stress, previously evaluated by Davies and Unruh (1977) to be equivalent to the conventional fermion stress tensor (in the absence of compact spatial sections).