From conformal quantum mechanics on bordered Riemann surfaces to covariant string field theory

Abstract

The Faddeev-Popov determinant of the reparametrization ghosts of the closed bosonic string on bordered Riemann surfaces is investigated. It is found that the standard ghost action has to be supplemented by additional boundary terms. These additional terms lead to a nontrivial ghost transition amplitude. It is shown that boundary variations of ghost transition amplitudes are generated by the ghost Virasoro operators. The relevance of the boundary variation operator for string field theory is illustrated. A new interpretation of the BRST operator in terms of boundary variations is obtained and the BRST invariance of the transition amplitudes is demonstrated. A generalization of the Siegel gauge of second quantized closed bosonic string field theory is presented.