Duality of the Dirichlet and Neumann problems in braneworld physics

TL;DR

This paper explores the duality between Dirichlet and Neumann boundary value problems in braneworld physics, demonstrating their equivalence through boundary operator relations in a two-brane model.

Contribution

It establishes a duality relation linking Dirichlet and Neumann problems, providing a unified approach to braneworld effective action construction.

Findings

Demonstrates equivalence of Dirichlet and Neumann methods

Identifies duality relations between boundary operators

Provides a new perspective on braneworld effective actions

Abstract

Braneworld effective action for two-brane model is constructed by two different methods based respectively on the Dirichlet and Neumann boundary value problems. The equivalence of these methods is shown due to nontrivial duality relations between special boundary operators of these two problems.