  It was recently discovered that for a boundary system in the presence of a
background magnetic field, the quantum fluctuation of the vacuum would create a
non-uniform magnetization density for the vacuum and a magnetization current is
induced in the vacuum. It was also shown that this magnetic Casimir effect of
the vacuum is closely related to another quantum effect of the vacuum, the Weyl
anomaly. Furthermore, the phenomena can be understood in terms of the
holography of the boundary system. In this article, we review the derivation of
this phenomena from QFT as well as the derivation of it using AdS/BCFT. We then
generalize this four dimensional effect to six-dimensions. We use the AdS/BCFT
holography to show that in the presence of a 3-form magnetic field strength
$H$, a string current is induced in a six-dimensional boundary conformal field
theory. This allows us to determine the gauge field contribution to the Weyl
anomaly in six-dimensional conformal field theory in a $H$-flux background. For
the (2,0) superconformal field theory of $N$ M5-branes, the current has a
magnitude proportional to $N^3$ for large $N$. This suggests that the degree of
freedoms scales as $N^3$ in the (2,0) superconformal theory of $N$ multiple
M5-branes. Our result for the Weyl anomaly is a new prediction for the (2,0)
theory.

High Energy Physics - Theory