[Paper Review] Worldvolume Supersymmetry

Рената Каллош|arXiv (Cornell University)|Sep 9, 1997

Black Holes and Theoretical Physics3 references4 citations

TL;DR

This paper establishes a general framework to convert local kappa-symmetry and spacetime supersymmetry into global worldvolume supersymmetry for branes, using a Killing spinor-adapted gauge for kappa-symmetry. It applies this method to the M5-brane, successfully gauge-fixing its action to obtain the (0,2) tensor multiplet in six dimensions, confirming consistency with known supermultiplet structure.

ABSTRACT

A general set of rules is given how to convert a local kappa-symmetry of a brane action and space-time supersymmetry into the global supersymmetry of the worldvolume. A Killing spinor adapted gauge for quantization of kappa-symmetry is defined for this purpose. As an application of these rules we perform the gauge-fixing of the M-5-brane to get the theory of the (0, 2) tensor supermultiplet in d=6.

Motivation & Objective

• To derive a general procedure for converting local kappa-symmetry and spacetime supersymmetry into global worldvolume supersymmetry.
• To resolve the challenge of consistently quantizing brane actions with both kappa-symmetry and spacetime supersymmetry.
• To provide a systematic method applicable to higher-dimensional branes, particularly the M5-brane.
• To demonstrate the emergence of the (0,2) tensor supermultiplet in six dimensions from the M5-brane action.

Proposed method

• Introduce a Killing spinor-adapted gauge choice for kappa-symmetry to simplify the quantization procedure.
• Use the interplay between spacetime supersymmetry and local kappa-symmetry to identify the global worldvolume supersymmetry algebra.
• Apply the gauge-fixing procedure to the M5-brane action in a way that preserves manifest spacetime supersymmetry.
• Derive the resulting worldvolume theory and verify that it describes the (0,2) tensor multiplet in six dimensions.
• Ensure consistency of the gauge-fixed action with known supermultiplet content and field content.
• Use the standard formulation of the M5-brane action with a self-dual three-form field strength as input.

Experimental results

Research questions

• RQ1 How can local kappa-symmetry and spacetime supersymmetry be systematically converted into global worldvolume supersymmetry?
• RQ2 What gauge choice for kappa-symmetry enables consistent quantization and preserves spacetime supersymmetry?
• RQ3 Does the gauge-fixed M5-brane action yield the correct (0,2) tensor supermultiplet in six dimensions?
• RQ4 What is the role of Killing spinors in defining a consistent gauge for kappa-symmetry?
• RQ5 How does the worldvolume theory of the M5-brane realize the (0,2) supermultiplet structure?

Key findings

• The proposed method successfully converts kappa-symmetry and spacetime supersymmetry into global worldvolume supersymmetry for branes.
• The Killing spinor-adapted gauge choice provides a consistent framework for gauge-fixing kappa-symmetry in the M5-brane action.
• The gauge-fixed M5-brane action describes the (0,2) tensor supermultiplet in six dimensions, as required by supermultiplet theory.
• The resulting worldvolume theory preserves the correct number of supersymmetries and field content for the (0,2) multiplet.
• The derivation confirms that the M5-brane action, when properly gauge-fixed, yields a consistent six-dimensional super-Yang-Mills-like theory with (0,2) supersymmetry.
• The work provides a generalizable procedure applicable to other branes and dimensions, extending the understanding of worldvolume supersymmetry.