D-Branes in Coset Models

TL;DR

This work develops a general reduction from branes on group manifolds to D-branes in coset models $G/H$, yielding constrained non-commutative gauge theories that describe coset brane dynamics in a large-$k$ regime. Brane configurations labeled by representations of ${\mathfrak g}\oplus{\mathfrak h}$ condense to other configurations whenever their diagonal ${\mathfrak h}_{\rm diag}$ restrictions match, implying conserved charges live in the representation ring of the denominator ${\mathfrak h}$. The authors derive explicit effective actions for coset branes, demonstrate a wide class of condensation solutions, and apply the framework to parafermions and ${\cal N}=2$ minimal models to reveal geometric and RG-flow interpretations of boundary states. The results connect non-commutative gauge theory, coset CFT, and brane geometry, offering a robust tool to analyze boundary theories and brane dynamics in exact solvable backgrounds with potential extensions to finite $k$ and twined-brane setups.

Abstract

The analysis of D-branes in coset models G/H provides a natural extension of recent studies on branes in WZW-theory and it has various interesting applications to physically relevant models. In this work we develop a reduction procedure that allows to construct the non-commutative gauge theories which govern the dynamics of branes in G/H. We obtain a large class of solutions and interprete the associated condensation processes geometrically. The latter are used to propose conservation laws for the dynamics of branes in coset models at large level k. In super-symmetric theories, conserved charges are argued to take their values in the representation ring of the denominator theory. Finally, we apply the general results to study boundary fixed points in two examples, namely for parafermions and minimal models.

Figures (3)

• Figure 2: Geometric interpretation: The picture shows the underlying geometry of the minimal models together with the possible point-like branes of the form $[L,0]$ sitting at the top and at the bottom of a cylinder with squeezed ends. The right end of the cylinder is cut.
• Figure 3: Processes in the minimal model geometry of Fig. \ref{['fig:mmodgeometry']} with removed front wall. Two processes are shown: (a) A one-dimensional string-like brane $(0,7)$ decays into one point-like brane at the top. (b) A two-dimensional brane $(2,4)$ decays into a configuration of point-like branes at the bottom.
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