Some Computations of Partition Functions and Tachyon Potentials in Background Independent Off-Shell String Theory

TL;DR

The paper investigates what information about tachyon potentials and background fields can be reliably extracted from background independent off-shell string theory (BIOST) when world-sheet renormalization conditions are not fully specified. It introduces a universality principle—renormalization-scheme independence—to isolate universal features, and analyzes tachyon and gauge backgrounds in both bosonic and fermionic (supersymmetric) strings across multiple renormalization schemes. The authors derive universal asymptotics for the partition function in terms of the combination u = (1+f)^{-1}t, demonstrate that the two BIOST action definitions share the same universal content in the bosonic case, and show that the resulting tachyon/gauge potentials reproduce Born-Infeld-type effective actions (with supersymmetric analogues) up to non-universal derivative terms. These results provide a scheme-independent window into open-string dynamics and tachyon condensation, and connect to noncommutative structures in certain limits, highlighting the robustness of the universal content of BIOST-derived potentials.

Abstract

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 for. It turns out that some asymptotics which are responsible for the potentials only obey the principle of universality.