U(1) gauge invariance from open string field theory

TL;DR

The paper demonstrates that the low-energy action for the open string tachyon and U(1) gauge field obtained from string field theory does not match the world-volume action of unstable branes, but that a field redefinition between string-field variables and world-volume fields exists to the first non-linear order. It identifies a string gauge symmetry that corresponds to the conventional U(1) gauge transformation and derives three consistency conditions (A,B,C) for the field redefinition, showing these are identically satisfied and constructing explicit solutions in three cases. Through level-truncation analysis, it studies the vector (transverse photon) excitations at the tachyon condensate, finding a physical vector at (3,6) but uncertainty about its fate at (4,8), and showing the kinetic term evolves slowly with truncation, indicating the world-volume DBI action does not arise directly without redefinition. Collectively, the results clarify how DBI-like physics emerges from string field theory only after a nontrivial redefinition and reveal a larger gauge structure rooted in string field theory that governs the open string sector of unstable branes.

Abstract

The naive low energy effective action of the tachyon and the U(1) gauge field obtained from string field theory does not correspond to the world volume action of unstable branes in bosonic string theory. We show that there exists a field redefinition which relates the gauge field and the tachyon of the string field theory action to the fields in the world volume action of unstable branes. We identify a string gauge symmetry which corresponds to the U(1) gauge transformation. This is done to the first non-linear order in the fields. We examine the vector fluctuations at the tachyon condensate till level (4,8).