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arXiv 1111.4822hep-thgr-qc
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非对易引力与费米子耦合：Seiberg-Witten映射的二阶展开

Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map

Paolo Aschieri, Leonardo Castellani

备注：
27 pages, LaTeX. Revised version with proof of charge conjugation symmetry of the NC action and its parity under theta --> - theta (see new sect. 2.6, sect. 6 and app. B). References added. arXiv admin note: substantial text overlap with arXiv:0902.3817
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摘要：

我们使用Seiberg-Witten映射（SW映射）来展开耦合到费米子的非对易引力。该作用量在一般坐标变换和局部洛仑兹旋转下是不变的，并且具有与交换引力作用量相同的自由度。在非对易性参数θ下给出了二阶展开式。的SW映射的几何重新制定和推广，适用于任何阿贝尔扭曲。证明了该映射与厄米性和电荷共轭条件的相容性。证明了作用量是实的，在θ中的所有阶电荷共轭下都是不变的。这意味着作用量的玻色子部分在θ中是偶数，而马约拉纳费米子的费米子部分在θ中是偶数。

英文摘要：

We use the Seiberg-Witten map (SW map) to expand noncommutative gravity coupled to fermions in terms of ordinary commuting fields. The action is invariant under general coordinate transformations and local Lorentz rotations, and has the same degrees of freedom as the commutative gravity action. The expansion is given up to second order in the noncommutativity parameter θ. A geometric reformulation and generalization of the SW map is presented that applies to any abelian twist. Compatibility of the map with hermiticity and charge conjugation conditions is proven. The action is shown to be real and invariant under charge conjugation at all orders in θ. This implies the bosonic part of the action to be even in θ, while the fermionic part is even in θ for Majorana fermions.

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