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arXiv 2104.01020cond-mat.supr-congr-qchep-ph
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拓扑手征超导体中引力反常的模拟

Analog of gravitational anomaly in topological chiral superconductors

G. E. Volovik

摘要:

众所周知,扭转对手征外尔费米子方程的贡献可以等效地用轴向$U(1)$规范场来考虑。在这种情况下,引力场转换为$U(1)$规范场。在这里,我们表明,在手征超导体相反的情况下发生:电磁$U(1)$场作为自旋连接的Bogoliubov费米子准粒子。结果,电磁场引起重力异常,与常规手征异常相比,在相应的Adler-Bell-Jackiw方程中含有额外的因子$1/3$。我们还考虑了中性外尔超流体中产生的引力异常,它类似于引力瞬子,即三维拓扑物体--引力瞬子导致手征电荷的产生。

英文摘要:

It is known that the contribution of torsion to the equation for the chiral Weyl fermions can be equivalently considered in terms of the axial $U(1)$ gauge field. In this scenario the gravitational field transforms to the $U(1)$ gauge field. Here we show that in chiral superconductors the opposite scenario takes place: the electromagnetic $U(1)$ field serves as the spin connection for the Bogoliubov fermionic quasiparticles. As a result the electromagnetic field gives rise to the gravitational anomaly, which contains the extra factor $1/3$ in the corresponding Adler-Bell-Jackiw equation as compared with the conventional chiral anomaly. We also consider the gravitational anomaly produced in neutral Weyl superfluids by the analog of the gravitational instanton, the process of creation and annihilation of the 3D topological objects -- hopfions. The gravitational instanton leads to creation of the chiral charge.

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