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Brane Dynamics in CFT Backgrounds

Stefan Fredenhagen, Volker Schomerus

TL;DR

This work analyzes bound-state formation and decay of branes in non-trivial backgrounds by combining boundary conformal field theory with decoupling-limit (non-commutative) gauge theories on brane world-volumes. Starting from branes on group manifolds such as $S^3 \\\cong \\mathrm{SU}(2)$, it derives a fuzzy-sphere description in the large-$k$ limit and an effective action ${\\cal S}_{(Q,\\alpha)} = {\\cal S}_{YM} + {\\cal S}_{CS}$ that governs condensates, including a key decay channel where $Q$ point-branes condense into a single brane of type $\\alpha=(Q-1)/2$. Extending these ideas to parafermion theories and $N=2$ minimal models via cosets, the paper identifies similar bound-state structures and computes the corresponding reduced actions, highlighting a robust RG-flow picture and a topological charge classification provided by twisted K-theory $K^*_H(SU(2)) = \\mathbb{Z}_K$. The results establish a coherent framework linking geometric brane configurations, non-commutative gauge dynamics, and topological charges, with implications for Gepner models and broader CFT backgrounds.

Abstract

In this note we discuss bound states of un- or meta-stable brane configurations in various non-trivial (curved) backgrounds. We begin by reviewing some known results concerning brane dynamics on group manifolds. These are then employed to study condensation in cosets of the WZW model. While the basic ideas are more general, our presentation focuses on parafermion theories and, closely related, N=2 superconformal minimal models. We determine the (non-commutative) low energy effective actions for all maximally symmetric branes in a decoupling limit of the two theories. These actions are used to show that the lightest branes can be regarded as elementary constituents for all other maximally symmetric branes.

Brane Dynamics in CFT Backgrounds

TL;DR

This work analyzes bound-state formation and decay of branes in non-trivial backgrounds by combining boundary conformal field theory with decoupling-limit (non-commutative) gauge theories on brane world-volumes. Starting from branes on group manifolds such as , it derives a fuzzy-sphere description in the large- limit and an effective action that governs condensates, including a key decay channel where point-branes condense into a single brane of type . Extending these ideas to parafermion theories and minimal models via cosets, the paper identifies similar bound-state structures and computes the corresponding reduced actions, highlighting a robust RG-flow picture and a topological charge classification provided by twisted K-theory . The results establish a coherent framework linking geometric brane configurations, non-commutative gauge dynamics, and topological charges, with implications for Gepner models and broader CFT backgrounds.

Abstract

In this note we discuss bound states of un- or meta-stable brane configurations in various non-trivial (curved) backgrounds. We begin by reviewing some known results concerning brane dynamics on group manifolds. These are then employed to study condensation in cosets of the WZW model. While the basic ideas are more general, our presentation focuses on parafermion theories and, closely related, N=2 superconformal minimal models. We determine the (non-commutative) low energy effective actions for all maximally symmetric branes in a decoupling limit of the two theories. These actions are used to show that the lightest branes can be regarded as elementary constituents for all other maximally symmetric branes.

Paper Structure

This paper contains 6 sections, 16 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Semi-classical geometry of branes on $S^3$
  3. Decoupling limit and fuzzy gauge theories
  4. Dynamics in stringy regime and K-theory
  5. Brane dynamics in parafermion theories
  6. Outlook and further directions

Figures (2)

  • Figure 1: Brane dynamics on $S^3$: A stack of point-like branes at $e$ can decay into a single spherical object. The distance of the latter increases with the number of branes in the stack until one obtains a single point-like object at $-e$.
  • Figure :