Holographic BCFT with Dirichlet Boundary Condition

TL;DR

This paper demonstrates that Dirichlet boundary conditions are viable in holographic BCFT, producing key physical features and solutions, including boundary currents, with potential experimental implications.

Contribution

It shows Dirichlet boundary conditions are as effective as Neumann in holographic BCFT, including solutions and physical predictions, expanding the boundary condition options.

Findings

Dirichlet BC includes AdS solutions and obeys the g-theorem.

Correctly reproduces boundary Weyl anomaly and one-point functions.

Magnetic charge black hole induces boundary currents, suggesting experimental tests.

Abstract

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-Nordstrom 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.