Moduli Space of Unstable D-branes on a Circle of Critical Radius

TL;DR

This paper analyzes the moduli space of unstable D-branes on a circle at critical radius, comparing conformal field theory and tachyon effective field theory, revealing similar structures and supporting the latter's qualitative accuracy.

Contribution

It identifies and compares the moduli space structures of boundary conformal field theories and tachyon effective field theories for unstable D-branes on a circle at critical radius.

Findings

The moduli space has two branches: a 3D S^3/Z_2 and a 2D T^2.

The two branches are joined along a circle.

The tachyon effective field theory reproduces the moduli space structure with a deformed S^3.

Abstract

We study the moduli space of the boundary conformal field theories describing an unstable D-brane of type II string theory compactified on a circle of critical radius. This moduli space has two branches, -- a three dimensional branch S^3/Z_2 and a two dimensional branch described by a square torus T^2. These two branches are joined along a circle. We compare this with the moduli space of classical solutions of tachyon effective field theory compactified on a circle of critical radius. This moduli space has a very similar structure to that of the boundary conformal field theory with the only difference that the S^3 of the S^3/Z_2 component becomes a deformed S^3. This provides one more indication that the tachyon effective field theory captures qualitatively the dynamics of the tachyon on an unstable D-brane.