Weyl Anomaly and Vacuum Magnetization Current of M5‐brane in Background Flux

Abstract

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 N3 for large N. This suggests that the degree of freedoms scales as N3 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.

Fermion condensation induced by the Weyl anomaly

“…to the leading order of small σ. Generalization of the result (2) to higher dimensions and the result (3) for arbitrary finite σ can be found in [6][7][8] respectively. We remark that these anomalous currents do not rely on the presence of a material system, but is a pure vacuum phenomena.…”

“…where n denotes the internal normal of the manifold M. Next, we substitute (7) into the rhs of (8), integrate over x and select the logarithmic divergent term, we obtain Z…”

Enhancement of anomalous boundary current by high temperature

“…It is similar to the anomaly-induced transport [8,9] such as chiral magnetic effect (CME) [10][11][12][13][14] and chiral vortical effect (CVE) [15][16][17][18][19][20][21]. See also [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] for related works.…”

“…which exactly agrees with (22,24). Substituting ( 26) into ( 25), we re-derive (23). As in the high temperature limit, the sum can be replaced by the following integral lim…”

Conformal boundary condition and massive gravitons in AdS/BCFT

“…The intimate connection of the Weyl anomaly to the Casimir effects has been generalized to higher dimensions [60], to anomalous currents [61][62][63][64] and Fermion condensations [65,66]. Due to the boundary, the energy moment tensor of BCFT is no longer conserved generally.…”