Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
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DOI：
10.3390/sym13112019
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发表时间：
2021-07
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通讯作者：
Victor E. Ambruş;E. Winstanley
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文献类型：
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作者：
Victor E. Ambruş;E. Winstanley
本文研究反德西特空间中有限温度下刚性转动的量子费米子场。我们假设旋转速率Ω小于曲率半径的倒数<$−1，因此没有光速表面，静态（最大对称）和旋转真空重合。这个假设使我们能够遵循几何方法，采用封闭形式的真空两点函数的表达式，然后可以用来计算热期望值（t. e. v. s）。在高温区，我们发现了一个完美的类比与闵可夫斯基时空的已知结果，揭示曲率效应的形式涉及里奇标量R的额外条款。验证了轴向涡旋效应的有效性，发现对于无质量费米子，轴向通量通过二维切片逃逸到无穷远，而对于有质量费米子，轴向通量完全转化为赝标密度−i <$$> γ5 <$。最后，我们讨论了体积性质，如时空中的总标量凝聚和总能量，并证明它们在极限Ω→ Ω −1时发散为[1− <$2 Ω2]−1。
Here, we study a quantum fermion field in rigid rotation at finite temperature on anti-de Sitter space. We assume that the rotation rate Ω is smaller than the inverse radius of curvature ℓ−1, so that there is no speed of light surface and the static (maximally-symmetric) and rotating vacua coincide. This assumption enables us to follow a geometric approach employing a closed-form expression for the vacuum two-point function, which can then be used to compute thermal expectation values (t.e.v.s). In the high temperature regime, we find a perfect analogy with known results on Minkowski space-time, uncovering curvature effects in the form of extra terms involving the Ricci scalar R. The axial vortical effect is validated and the axial flux through two-dimensional slices is found to escape to infinity for massless fermions, while for massive fermions, it is completely converted into the pseudoscalar density −iψ¯γ5ψ. Finally, we discuss volumetric properties such as the total scalar condensate and the total energy within the space-time and show that they diverge as [1−ℓ2Ω2]−1 in the limit Ω→ℓ−1.