Tachyon Condensation and Brane Descent Relations in p-adic String Theory

TL;DR

The paper tests the tachyon-condensation paradigm in a solvable setting by using the exact tree-level action of $p$-adic open strings to realize the vacuum without D-branes and to construct translationally localized lump solutions as lower-dimensional D-branes. It derives the world-volume theory on solitonic $q$-branes, showing that tachyon fluctuations obey a nonlocal kinetic equation and that the effective action matches that of Dirichlet $q$-branes, including explicit amplitude equivalences. The results provide strong evidence that p-adic lump solutions implement brane descent and that brane tensions and self-dual radii align with the expected D-brane picture, offering a tractable toy model for tachyon condensation and potential connections to ordinary bosonic string theory.

Abstract

It has been conjectured that an extremum of the tachyon potential of a bosonic D-brane represents the vacuum without any D-brane, and that various tachyonic lump solutions represent D-branes of lower dimension. We show that the tree level effective action of p-adic string theory, the expression for which is known exactly, provides an explicit realisation of these conjectures.

Figures (2)

• Figure 1: The effective tachyon potential for the $p$-adic string.
• Figure 2: The Feynmann diagrams contributing to the amplitude $\langle\sigma\sigma\chi\chi\rangle$ on the solitonic $q$-brane. A dashed line denotes the $\chi$ propagator and a solid line denotes the $\sigma$ propagator.