On Superconnections and the Tachyon Effective Action

TL;DR

This paper presents a geometric tachyon effective action for brane–antibrane and non-BPS Dp-branes based on superconnections and their supercurvature. The proposed DBI+WZ framework yields tachyon potentials $V(T,\bar{T})\sim e^{-T\bar{T}}$ (brane–antibrane) and $V(T)\sim e^{-T^2}$ (non-BPS), and reproduces RR couplings via the WZ term. Tachyon condensation is analyzed through kink and vortex solutions with infinite constant gauge-field strength, yielding exact lower-dimensional D-brane tensions $T_{p-1}$ and $T_{p-2}$, respectively. The work discusses its relation to BSFT and other models, noting that equivalence may require field redefinitions at fixed points and within the slowly varying-field approximation, thereby offering a K-theory–inspired, superconnection perspective on tachyon dynamics and brane descent relations.

Abstract

We propose a form of the effective action of the tachyon and gauge fields for brane-antibrane systems and non-BPS Dp-branes, written in terms of the supercurvature. Kink and vortex solutions with constant infinite gauge field strength reproduce the exact tensions of the lower-dimensional D-branes. We discuss the relation to BSFT and other models in the literature.