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-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.
Highlights
Where n denote the normal direction, i denote the tangent direction and ∗F is the Hodge dual of the field strength F
We have investigated the holographic BCFT with Dirichlet BC and find it works as well as the one with Neumann BC
It is remarkable that the boundary central charge related to B-type Weyl anomaly, or equivalently, the Casimir coefficient for Dirichlet BC is less than or equal to the one for Neumann BC
Summary
We study the BCs of Maxwell fields in holographic BCFT. This can be regarded as a warm-up for the gravitational case. We find that both absolute BC and relative BC can yield the expected asymptotic behaviors of one point function of current near the boundary. Both BCs can reproduce the universal relations between the current and Weyl anomaly
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