Tachyon condensation using the disc partition function

TL;DR

The paper tests the conjecture that the background independent open superstring field theory action is given by the disc partition function with boundary operators by analyzing tachyon condensation in the D0–D2 system under a large NS-NS B-field. It builds boundary tachyon operators using twist fields, computes the disc partition function perturbatively up to quartic order in the almost marginal boundary coupling, and derives the mass defect from this partition function. The main result is that the leading mass defect, obtained from the disc partition function, exactly matches the BPS prediction in the large B-field limit, ΔM = -\frac{1}{2\sqrt{2} g b^2}. This agreement provides strong support for the disc partition function proposal as the correct background independent action and demonstrates a viable perturbative framework for twisted-sector tachyon condensation, with implications for comparisons to Berkovits-type string field theory.

Abstract

It has been recently proposed that the background independent open superstring field theory action is given by the disc partition function with all possible open string operators inserted at the boundary of the disc. We use this proposal to study tachyon condensation in the D0-D2 system. We evaluate the disc partition function for the D0-D2 system in presence of a large Neveu-Schwarz B-field using perturbation theory. This perturbative expansion of the disc partition function makes sense as the boundary tachyon operator for the large Neveu-Schwarz B-field is almost marginal. We find that the mass defect for the formation of the D0-D2 bound state agrees exactly with the expected result in the large B-field limit.