Duality of boundary value problems and braneworld action in curved brane models

TL;DR

This paper explores the duality between boundary value problems in curved brane models and constructs the effective braneworld action using two methods, extending previous algorithms to curved geometries like deSitter and Anti-deSitter.

Contribution

It demonstrates the equivalence of Dirichlet and Neumann boundary approaches via duality relations and generalizes braneworld action algorithms to curved branes.

Findings

Established duality relations between boundary operators.

Unified effective action construction for curved branes.

Extended algorithms to deSitter and Anti-deSitter geometries.

Abstract

Braneworld effective action 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. Previously known braneworld action algorithms in two-brane Randall-Sundrum model are generalized to curved branes with deSitter and Anti-deSitter geometries.