Boundary string current &amp; Weyl anomaly in six-dimensional conformal field theory

Chu, Chong‐Sun; Miao, Rong-Xin

doi:10.1007/jhep07(2019)151

Cited by 9 publications

(14 citation statements)

References 116 publications

(162 reference statements)

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“…Finally, we extend our discussions to n-form fields and find similar anomalous currents. We notice that our results agree with Type II anomalous current for the two-form field [20,21]. For simplicity, in this paper we discuss only the current induced by an external electromagnetic field in four dimensions.…”

Section: Conclusion and Discussionsupporting

confidence: 84%

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Anomalous current due to Weyl anomaly for conformal field theory

Zheng

Zeng

et al. 2019

Physics Letters B

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Recently it is found that Weyl anomaly leads to new anomalous currents in an external electromagnetic field in a curved spacetime. For simplicity, the initial works mainly focus on weak gravitational fields and the anomalous current is obtained for conformally flat spaces with small scale factors. In this paper, we generalize the results to the case with arbitrary scale factors. Firstly, we derive the transformation law of current under Weyl transformation, from which one can read off the anomalous current in general conformally flat spaces. Secondly, by using the Weyl transformation of currents we provide a new derivation of the Weyl-anomaly-induced current near the boundary. Thus we have obtained the two kinds of anomalous currents in the literature from a unified formula. Finally, we extend the discussions to n-form fields and find similar anomalous currents. *

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Section: Conclusion and Discussionsupporting

confidence: 84%

“…where x is the distance to the boundary and ... denotes higher orders of O(x). Note that (55) agrees with the result of [20,21] for two-form fields. This can be regarded as a check of our results.…”

Section: Field-theoretical Methodssupporting

confidence: 89%

Anomalous current due to Weyl anomaly for conformal field theory

Zheng

Zeng

et al. 2019

Physics Letters B

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“…couples to the other fields of the system. For example in

d = 6

, we have the relation

{(δ A)}_{M_{ε}} = {(\int_{M_{ε}} \sqrt{g} J^{μ ν} δ B_{μ ν})}_{\log \frac{1}{ε}} .

Using the holographic result , one can verify that [] is satisfied with

scriptA

given by

A = \int_{M} \sqrt{g} \frac{b}{6} H_{μ ν λ}^{2}

Note that one can also use the AdS/BCFT to compute the holographic stress tensor and the Weyl anomaly . The same result is obtained.…”

Section: Weyl Anomaly and Induced Current For Six‐dimensional Cftsupporting

confidence: 55%

“…

scriptB

is the bulk gauge field whose boundary value is given by the gauge field B on the boundary M . The induced current can be calculated in a similar way as above and we obtain

false⟨ J^{a b} false⟩ = \lim_{z \to 0} \frac{δ I}{δ {scriptB}_{a b}} = b \frac{H_{x a b}}{x},

where

b = - \frac{R^{5}}{16 π G_{N}}

is a constant. As in the four dimensional case, the current is independent of boundary condition.…”

Section: Holographic Boundary Currentmentioning

confidence: 96%

“…To this end, a novel approach was adopted in the paper. [53] There a boundary was introduced to the M5-brane system. By using a holographic duality for BCFT, [54][55][56] it was found 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.…”

Section: The Proposed Self-duality Equation Readsmentioning

confidence: 99%

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

Chu

2019

Fortschritte der Physik

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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.

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Conformal boundary condition and massive gravitons in AdS/BCFT

Chu

Miao

2022

J. High Energ. Phys.

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According to Witten [1], the conformal boundary condition of gravity, which specifies the conformal geometry of the boundary and the trace of the extrinsic curvature, is elliptic and leads to well-defined perturbation theory of gravity about any classical solution. The conformal boundary condition was previously considered in [2, 3] in the context of AdS/BCFT, wherein the equation of motion of the end-of-the-world was derived and emphasized. In this paper, we investigate further other consequences of the conformal boundary condition in AdS/BCFT. We derive the boundary central charges of the holographic Weyl anomaly and show that they are exactly the same for conformal boundary condition and Dirichlet boundary condition. We analysis the metric perturbation with conformal boundary condition (CBC), Dirichlet boundary condition (DBC) and Neumann boundary condition (NBC) imposed on the end-of-the-world brane and show that they admit an interpretation as the fluctuation of the extrinsic curvature (case of CBC and DBC) and the induced metric (case of NBC) of Q respectively. In all cases, the fluctuation modes are massive, which are closely relevant to the massive island formation in the literature. Our results reveal that there are non-trivial gravitational dynamics from extrinsic curvatures on the conformal and Dirichlet branes, which may have interesting applications to the island. We also discuss, in passing, the localization of gravitons in brane world theory. We find that, contrary to NBC, the graviton for CBC/DBC is located on the brane with non-positive tension instead of non-negative tension.

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Boundary string current & Weyl anomaly in six-dimensional conformal field theory

Cited by 9 publications

References 116 publications

Anomalous current due to Weyl anomaly for conformal field theory

Anomalous current due to Weyl anomaly for conformal field theory

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

Conformal boundary condition and massive gravitons in AdS/BCFT

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