Holographic Anomalous Chiral Current Near a Boundary

2025-04-22 0 0 309.43KB 12 页 10玖币

侵权投诉

Rong-Xin Miao ∗, Yu-Qian Zeng

School of Physics and Astronomy, Sun Yat-Sen University, 2 Daxue Road, Zhuhai 519082,

China

Abstract

Due to the Weyl anomaly, an axial vector ﬁeld produces novel anomalous chiral cur-

rents in spacetime with boundaries. Remarkably, the chiral current is not invariant under

the gauge transformation of axial vector ﬁelds. As a result, more potential terms appear,

and the chiral current becomes larger than the electric current near the boundary. This

paper investigates the anomalous chiral current in AdS/BCFT. We ﬁnd that the minimal

holographic model of the axial vector ﬁeld cannot produce the expected chiral current.

To resolve this problem, we propose adding a suitable boundary action. Furthermore, we

notice a similar situation for holographic condensation. Finally, we obtain the shape de-

pendence of holographic chiral current and verify that it agrees with the ﬁeld-theoretical

result.

∗Email: miaorx@mail.sysu.edu.cn

arXiv:2210.05203v2 [hep-th] 12 Jan 2023

Contents

1 Introduction 1

2 Holographic condensation 2

3 Holographic chiral current 4

4 Shape dependence of holographic chiral current 5

5 Conclusions and Discussions 7

A Chiral current from Weyl anomaly 8

1 Introduction

Anomaly-induced transports are novel phenomena with wide applications in condensed mat-

ter, quantum ﬁeld theory, and cosmology [1]. The famous examples include the chiral mag-

netic eﬀect (CME) [2, 3, 4, 5, 6] and chiral vortical eﬀect (CVE) [7, 8, 9, 10, 11, 12, 13], which

originated from the chiral anomaly. See also [14, 15, 16, 17, 42, 19, 20, 21, 22, 23, 24, 25,

26, 27, 28] for related works. Recently, it has been found that the Weyl anomaly [29] leads

to novel anomalous currents [30, 31], Fermi condensations [32, 33] and chiral currents [34]

in spacetime with boundaries. Remarkably, the Weyl-anomaly-induced transports take uni-

versal forms near the boundary, which apply to not only conformal ﬁeld theory but also the

general quantum ﬁeld theory because the Weyl anomaly is well-deﬁned for general quantum

ﬁeld theory [29].

Take free Dirac ﬁeld as an example

S=ZM

√−g¯

ψiγµ∇µ−iVµ−iγ5Aµψ, (1)

where Vµand Aµare vectors and axial vectors, respectively. We impose the general chiral

bag boundary conditions [35, 36]

(1 + ieiθγ5γn)ψ|∂M = 0 (2)

where ndenotes the normal direction and θis a constant. At the leading order near the

boundary, various anomalous transports near the boundary are given by [30, 31, 32, 33]

current : hJµ

Vi=1

6π2

nνHνµ

x+O(ln x),(3)

condensation : h¯

ψψi=cos θ

4π2

x3+O(1/x2),(4)

chiral current : hJµ

Ai=−1

6π2

hµν Aν

x2+O(1/x),(5)

where H=dV denotes the ﬁeld strength of vectors, xis the distance to the boundary, nν

is the inward-pointing normal vector and hµν is the induced metric on the boundary. Note

that we take signature (−1,1,1,1) in this paper, which is diﬀerent from [34]. Note also that

the above results apply to x>, where is a cut-oﬀ. There are also boundary contributions

at x=to the current and chiral current, which make the total transports ﬁnite [30].

This paper studies the anomalous chiral current in AdS/BCFT [38]. We ﬁnd that the

minimal holographic model of axial vectors cannot reproduce the expected chiral current (5).

To resolve this problem, we propose adding a relevant boundary term, which is similar to the

case of holographic condensation. We also investigate the shape dependence of holographic

chiral current and verify that it obeys the non-trivial constraint from the Weyl anomaly.

The paper is organized as follows. To warm up, we ﬁrst discuss holographic condensation

in section 2. We ﬁnd that an additional boundary action is necessary in order to derive the

expected condensation. In section 3, we study a non-minimal holographic model of the axial

vector ﬁeld and derive the desired anomalous chiral current. In section 4, we investigate

the shape dependence of holographic chiral current. Finally, we conclude with some open

questions in section 5.

2 Holographic condensation

To warm up, we ﬁrst study holographic condensation in this section. Due to the novel

boundary eﬀects, the vacuum expectation of a scalar operator is non-zero [37]

hOi ∼ 1

x∆,(6)

where ∆ is the conformal dimension, and xis the distance to the boundary. For O=¯

ψψ

and ∆ = 3, (6) becomes the Fermi condensation (4). It is found in [39] that the minimal

holographic model cannot recover the result (6). Instead, one has to add a boundary action

on the end-of-the-world brane Q,

I=ZN

dd+1xp|g|R+d(d−1) −1

2∇µφ∇µφ+m2φ2+ 2 ZQ

dxdp|γ|K−T+ξ

2φ,(7)

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HolographicAnomalousChiralCurrentNearaBoundaryRong-XinMiao*,Yu-QianZengSchoolofPhysicsandAstronomy,SunYat-SenUniversity,2DaxueRoad,Zhuhai519082,ChinaAbstractDuetotheWeylanomaly,anaxialvectoreldproducesnovelanomalouschiralcur-rentsinspacetimewithboundaries.Remarkably,thechiralcurrentisnotinvariantun...

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