D-branes in the diagonal SU(2) coset

TL;DR

This paper studies D-branes in a specific SU(2) coset model, revealing the geometric structure of various branes, including a unique spacefilling brane and others of lower dimensions, within a 3D pillow-shaped target space.

Contribution

It provides a detailed geometric analysis of symmetry-preserving D-branes in the diagonal SU(2) coset, identifying their dimensions and the special spacefilling brane.

Findings

The target space is a 3D pillow with four corners.

The fractional brane is spacefilling and reaches all corners.

Other branes have dimensions 3, 1, and 0.

Abstract

The symmetry preserving D-branes in coset theories have previously been described as being centered around projections of products of conjugacy classes in the underlying Lie groups. Here, we investigate the coset where a diagonal action of SU(2) is divided out from SU(2)\times SU(2). The corresponding target space is described as a (3-dimensional) pillow with four distinguished corners. It is shown that the (fractional) brane which corresponds to the fixed point that arises in the CFT description, is spacefilling. Moreover, the spacefilling brane is the only one that reaches all of the corners. The other branes are 3, 1 and 0 - dimensional.