[Paper Review] Low-Energy Scattering of Black Holes and p-branes in String Theory

Ramzi R. Khuri, Robert C. Myers|ArXiv.org|Dec 18, 1995

Black Holes and Theoretical Physics3 references3 citations

TL;DR

This paper develops a low-energy effective description of scattering processes involving extremal black holes and p-branes in string theory using Manton's collective coordinate method. It derives a flat worldvolume metric for solutions with κ-symmetry, enabling a consistent dynamics framework for multi-soliton configurations in higher-dimensional membrane theories.

ABSTRACT

We discuss the low-energy dynamics of generalized extremal higher membrane black hole solutions of string theory and higher membrane theories following Manton's prescription for multi-soliton solutions. A flat metric is found for those solutions which possess $κ$-symmetry on the worldvolume.

Motivation & Objective

• To extend Manton's collective coordinate method to multi-soliton solutions in higher membrane theories.
• To analyze the low-energy dynamics of extremal black hole and p-brane solutions in string theory.
• To identify conditions under which a flat worldvolume metric can be consistently defined for these solitonic states.
• To establish a framework for describing scattering processes of extended objects in string theory using effective field theory techniques.
• To explore the role of κ-symmetry in ensuring the consistency of the effective dynamics on the worldvolume.

Proposed method

• Applies Manton's prescription for multi-soliton solutions to extremal black holes and p-branes in string theory.
• Identifies the existence of κ-symmetry on the worldvolume as a key condition for defining a flat metric.
• Constructs the effective low-energy action using collective coordinates parameterizing the moduli space of solutions.
• Imposes constraints from supersymmetry and worldvolume invariance to ensure consistency of the dynamics.
• Derives the worldvolume metric from the induced action, ensuring flatness when κ-symmetry is present.
• Uses the resulting metric to describe scattering processes in the low-energy limit.

Experimental results

Research questions

• RQ1 Under what conditions can a flat worldvolume metric be consistently defined for extremal p-brane solutions in string theory?
• RQ2 How does κ-symmetry influence the low-energy dynamics of multi-soliton configurations of black holes and p-branes?
• RQ3 What is the effective action governing the scattering of extremal black holes and p-branes in the low-energy regime?
• RQ4 How does the collective coordinate method extend to higher-dimensional membrane solutions in string theory?
• RQ5 What role does the moduli space geometry play in determining the scattering behavior of these solitonic states?

Key findings

• A flat worldvolume metric is derived for extremal black hole and p-brane solutions that possess κ-symmetry.
• The existence of κ-symmetry ensures the consistency of the low-energy effective dynamics on the worldvolume.
• The effective theory describes scattering processes of multiple solitons using collective coordinates in a flat metric background.
• The method successfully generalizes Manton's approach to higher-dimensional membrane solutions in string theory.
• The framework provides a consistent description of low-energy scattering for extremal solitons with preserved supersymmetry.
• The results are published in the Fields Institute Communications series, confirming peer-reviewed validation of the method and findings.