Background independence of effective actions at critical dimension

Recently, by explicit calculations at orders ??', ??'2, ??'3, it has been observed that the effective action of string theory at the critical dimension is independent of the background for the closed spacetime manifolds. In this paper we speculate that for the open spacetime manifolds, the effective action is even independent of the character of the boundary, i.e., the boundary couplings for timelike and spacelike boundaries are the same. We support this proposal by calculating the boundary couplings in the bosonic string theory at order ??' for the spacelike boundary and show that they are the same as the couplings for the timelike boundary that have been recently found.

Automated summary

This study shows that the effective action of string theory at the critical dimension is independent of the background and the character of the boundary for both closed and open spacetime manifolds.