Some computations of partition functions and tachyon potentials in background independent off-shell string theory

We discuss what information can be safely extracted from background independent off-shell string theory. The major obstacle in doing so is that renormalization conditions of the underlying world-sheet theories are not exactly known. To get some insight, we first consider the tachyon and gauge field backgrounds and carry out computations in different renormalization schemes for both, bosonic string and superstring. Next, we use a principle of universality (renormalization scheme independence) to somehow compensate the missing of the renormalization conditions and get information we are looking far. It turns out that some asymptotics which are responsible for the potentials only obey the principle of universality. (C) 2001 Elsevier Science B.V. All rights reserved.