Routing (electronic design automation)

Quantum mechanics

Robin boundary condition

Mathematical physics

Boundary (topology)

Boundary conformal field theory

Boundary value problem

Computer science

Dirichlet boundary condition

Neumann boundary condition

Computer network

Routing protocol

Physics

Mathematics

Quantum electrodynamics

Link-state routing protocol

Mathematical analysis

Conformal map

Black hole (networking)

Cauchy boundary condition

Mixed boundary condition

Journal of High Energy Physics

A bstract Neumann boundary condition plays an important role in the initial proposal of holographic dual of boundary conformal field theory, which has yield many interesting results and passed several non-trivial tests. In this paper, we show that Dirichlet boundary condition works as well as Neumann boundary condition. For instance, it includes AdS solution and obeys the g-theorem. Furthermore, it can produce the correct expression of one point function, the boundary Weyl anomaly and the universal relations between them. We also study the relative boundary condition for gauge fields, which is the counterpart of Dirichlet boundary condition for gravitational fields. Interestingly, the four-dimensional Reissner-Nordström black hole with magnetic charge is an exact solution to relative boundary condition under some conditions. This holographic model predicts that a constant magnetic field in the bulk can induce a constant current on the boundary in three dimensions. We suggest to measure this interesting boundary current in materials such as the graphene.

Holographic BCFT with Dirichlet boundary condition