[Paper Review] Decays of Four Intersecting Fluxbranes

Sunggeun Lee, Soonkeon Nam|ArXiv.org|Jul 1, 2006

Advanced Thermodynamics and Statistical Mechanics3 citations

TL;DR

This paper investigates the decay of four intersecting seven-dimensional fluxbranes (F7-branes) in M-theory, arising from a higher-dimensional Kerr black hole with four angular momentum parameters. Using Kaluza-Klein reduction and analysis of Killing vector fixed points, it identifies multiple decay channels into lower-dimensional spherical branes—such as 6-, 4-, 2-, and 0-branes—calculating the Euclidean action to determine decay rates, with divergences signaling supersymmetry protection under specific magnetic field relations.

ABSTRACT

We consider decays of four intersecting fluxbranes which are obtained by considering a higher dimensional Kerr blackhole with four angular momentum parameters, which is the maximum number of angular momentum parameters in string/M-theory. As a result of the intersection, we get lower dimensional fluxbranes. Since generic magnetic fields break all supersymmetries, the resulting fluxbranes are unstable and will decay. Just as a single fluxbrane decays into the nucleation of spherical D6-branes; the intersecting ones decay into the nucleation of lower dimensional spherical branes. Contrary to a single fluxbrane case, the decay of four intersecting fluxbranes has additional decay channels. We also calculate the corresponding Euclidean action to obtain the decay rates. Although the action cannot be explicitly and simply written in terms of the magnetic parameters, we can extract some interesting results by taking various limits of the magnetic parameters.

Motivation & Objective

• To investigate the decay mechanisms of four intersecting F7-branes in M-theory, which arise from a higher-dimensional Kerr black hole with maximal angular momentum parameters.
• To identify new decay channels beyond single or two-brane systems, particularly involving lower-dimensional spherical branes.
• To compute the Euclidean action for decay processes and determine decay rates, despite the lack of a simple closed-form expression in terms of magnetic parameters.
• To explore the role of Killing vector fixed points and spin structures in determining allowed decay modes and supersymmetry protection.

Proposed method

• Kaluza-Klein reduction of a higher-dimensional Kerr black hole with four angular momentum parameters to obtain four intersecting F7-branes.
• Analysis of fixed point sets of Killing vectors to identify possible decay products, such as spherical D-branes.
• Use of spin structure and partition function arguments to determine conditions under which supersymmetry is preserved (e.g., when magnetic fields satisfy $ B_1 = \pm B_2 \pm B_3 \pm B_4 $).
• Calculation of the Euclidean action for decay processes, with attention to divergences indicating instability or supersymmetry protection.
• Comparison of decay modes across different compactifications (e.g., type IIA vs. type 0A theories) by reducing along different Killing vector directions.
• Application of duality arguments to relate magnetic fluxbrane decays to electric brane systems and Dp–D̄p pair creation.

Experimental results

Research questions

• RQ1 What are the possible decay channels for four intersecting F7-branes in M-theory, and how do they differ from single or two-brane decay processes?
• RQ2 How does the Euclidean action for decay depend on the magnetic field parameters, and can it be explicitly computed in terms of these parameters?
• RQ3 Under what conditions on the magnetic fields does the decay amplitude diverge, and what does this imply for supersymmetry?
• RQ4 How do different compactifications (e.g., along one, three, or all four directions) lead to distinct types of string theories (IIA or 0A) and associated brane creation?
• RQ5 What is the role of the spin structure and fixed points of Killing vectors in determining the allowed decay products and their quantum stability?

Key findings

• The decay of four intersecting F7-branes produces multiple types of spherical branes, including 6-, 4-, 2-, and 0-branes, extending beyond the single D6-brane decay seen in the non-intersecting case.
• The Euclidean action diverges when the magnetic fields satisfy the relation $ B_1 = \pm B_2 \pm B_3 \pm B_4 $, signaling the presence of unbroken supersymmetry and suppression of decay.
• Decay modes depend on the choice of Killing vector reduction: reducing along one or three directions leads to type IIA theories, while reducing along two or four directions leads to type 0A theories.
• The action remains finite for generic magnetic field configurations, indicating a finite decay rate, except at specific symmetric points where supersymmetry protects the state.
• The results are consistent with the vanishing of the partition function under the same magnetic field conditions, confirming the absence of tachyonic modes when supersymmetry is preserved.
• The method provides a framework to study brane creation in intersecting fluxbrane backgrounds, with potential extension to electric-magnetic duals and time-dependent backgrounds like de Sitter.