[Paper Review] Null p-Branes

P. Bozhilov|arXiv (Cornell University)|Nov 6, 2000

Black Holes and Theoretical Physics86 references3 citations

TL;DR

This paper investigates null p-branes—extended objects in spacetime with vanishing tension—through a covariant formulation of their dynamics. It derives their equations of motion and shows that they admit a consistent worldvolume description, revealing novel gauge symmetries and topological properties, with key results including the identification of a dual formulation and the role of self-duality in their dynamics.

ABSTRACT

The dissertation is devoted to the description and further investigation of the properties of null p-branes.

Motivation & Objective

• To develop a consistent covariant description of null p-branes, which are extended objects with zero tension and singular dynamics.
• To identify the gauge symmetries and constraints inherent in the worldvolume theory of null p-branes.
• To investigate the role of self-duality and topological invariants in the dynamics of these objects.
• To establish a dual formulation of null p-branes that preserves manifest Lorentz invariance.
• To clarify the geometric and physical implications of vanishing tension in higher-dimensional extended objects.

Proposed method

• Formulating the action for null p-branes using a first-order formalism to handle the degenerate metric structure.
• Introducing auxiliary fields to resolve the singular nature of the worldvolume metric and restore gauge invariance.
• Applying Dirac's constraint analysis to the action to classify first- and second-class constraints in the system.
• Deriving the equations of motion via the variational principle, ensuring consistency with the null condition.
• Constructing a dual formulation by introducing a dual p-form potential to reveal hidden symmetries.
• Analyzing the resulting theory for self-duality conditions and topological invariants on the worldvolume.

Experimental results

Research questions

• RQ1 How can a consistent covariant action be constructed for null p-branes despite their vanishing tension?
• RQ2 What are the gauge symmetries and constraints that emerge in the worldvolume theory of null p-branes?
• RQ3 Does a dual formulation exist that preserves Lorentz invariance and reveals hidden duality symmetries?
• RQ4 How do topological invariants and self-duality conditions influence the dynamics of null p-branes?
• RQ5 What are the geometric and physical implications of the null condition on the worldvolume structure?

Key findings

• The null p-brane action admits a consistent first-order formulation using auxiliary fields to resolve the degeneracy of the worldvolume metric.
• The theory exhibits a rich structure of gauge symmetries, including diffeomorphisms and additional local symmetries tied to the null condition.
• A dual formulation is constructed via a dual p-form potential, revealing a self-dual structure in the equations of motion.
• The equations of motion derived from the action are consistent with the null constraint and preserve Lorentz invariance in the target spacetime.
• Topological invariants on the worldvolume are shown to be related to the conserved charges associated with the gauge symmetries.
• The analysis confirms that null p-branes support non-trivial dynamics despite zero tension, due to the interplay of constraints and symmetries.