Anomaly-free brane worlds in seven dimensions

Area of Science:

• Theoretical Physics
• String Theory
• Supergravity

Background:

• Minimal seven-dimensional supergravity theory provides a framework for unifying fundamental forces.
• Orbifold compactification is a key technique for reducing extra spatial dimensions in string theory.
• Anti-de Sitter space is a theoretical construct with constant negative spacetime curvature.

Purpose of the Study:

• To investigate an orbifold compactification of minimal seven-dimensional supergravity.
• To analyze the structure of the vacuum and the role of branes.
• To determine the implications of anomaly cancellation for gauge and gravitational properties.

Main Methods:

• Performing an orbifold compactification of the seven-dimensional supergravity theory.
• Analyzing the vacuum solution as a slice of anti-de Sitter space with specific brane configurations.
• Applying the principles of gauge and gravitational anomaly cancellation.

Main Results:

• The vacuum is identified as a slice of seven-dimensional anti-de Sitter space with six-branes at fixed points.
• Anomaly cancellation imposes constraints on the gauge group and matter content on the boundaries.
• Boundary gauge couplings are determined by the gravitational constant and Chern-Simons mass parameter.

Conclusions:

• Orbifold compactification in this supergravity model leads to a specific vacuum structure.
• Anomaly cancellation is crucial for consistency, dictating fundamental properties of the compactified theory.
• The study provides a framework for understanding boundary effects and couplings in higher-dimensional theories.