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arXiv 0902.3823hep-thgr-qcmath-phmath.MP
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D=3和D=4中的非对易超引力

Noncommutative supergravity in D=3 and D=4

Paolo Aschieri, Leonardo Castellani

摘要:

我们给出了一个非对易的D=3,N=1超引力,在双同态下不变,局部U(1,1)非对易的\star -规范变换和局部\star -超对称.它的交换极限是通常的D=3纯超引力,没有额外的场。同时得到了D=4,N=1超引力的非对易变形,在对易极限下,它退化为通常的简单超引力。它的作用量在非纯态和定域GL(2,C)\star -规范对称性下是不变的.交换作用的超对称性被非交换性破缺。局部\star -超对称不变性可以在具有手征引力子和复Vierbein的非对易D=4,N=1超引力中实现.

英文摘要:

We present a noncommutative D=3, N=1 supergravity, invariant under diffeomorphisms, local U(1,1) noncommutative \star-gauge transformations and local \star-supersymmetry. Its commutative limit is the usual D=3 pure supergravity, without extra fields. A noncommutative deformation of D=4, N=1 supergravity is also obtained, reducing to the usual simple supergravity in the commutative limit. Its action is invariant under diffeomorphisms and local GL(2,C) \star-gauge symmetry. The supersymmetry of the commutative action is broken by noncommutativity. Local \star-supersymmetry invariance can be implemented in a noncommutative D=4, N=1 supergravity with chiral gravitino and complex vierbein.

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