Gauge Fields and Fermions in Tachyon Effective Field Theories

TL;DR

This work embeds gauge fields and fermions into tachyon effective field theories for unstable D-branes, showing that gauge fluctuations on codimension-one kinks are discrete and localized, with no continuum on the tachyon vacuum. Using both superstring and bosonic models, the authors derive gauge couplings that preserve solvability and yield spectra that closely mirror open-string modes on D-branes, including a massless vector localized on the brane and infinite towers of massive excitations. They demonstrate fermion localization on Type II kinks, achieving eight massless fermions and bose–fermi degeneracy at the massless level, and extend the analysis to higher-derivative actions that retain solvability and allow higher-codimension branes. The results support a stringy-type spectrum emerging from simple scalar-gauge-fermion interactions on tachyon solitons, offering a tractable bridge between tachyon EFTs and full string-theoretic D-brane physics, while highlighting areas where exact descent relations require further clarification.

Abstract

In this paper we incorporate gauge fields into the tachyon field theory models for unstable D-branes in bosonic and in Type II string theories. The chosen couplings yield massless gauge fields and an infinite set of equally spaced massive gauge fields on codimension one branes. A lack of a continuum spectrum is taken as evidence that the stable tachyon vacuum does not support conventional gauge excitations. For the bosonic string model we find two possible solvable couplings, one closely related to Born-Infeld forms and the other allowing a detailed comparison to the open string modes on bosonic D-branes. We also show how to include fermions in the type II model. They localize correctly on stable codimension one branes resulting in bose-fermi degeneracy at the massless level. Finally, we establish the solvability of a large class of models that include kinetic terms with more than two derivatives.