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arXiv 2307.16624hep-th
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具有SU(1,n)时空对称性的费米子

Fermions with $SU(1,n)$ Spacetime Symmetry

Joseph Smith

AI总结:

本文通过零约化构造了具有SU(1,n)时空对称性的(2n-1)维自由费米子理论,利用超对称性确定两点函数并通过重求和恢复完整2n维结果,同时揭示了伽利略与卡罗尔场论在不同极限下的出现。

摘要:

我们通过将费米子在2n维Ω形变Minkowski背景上进行零约化,构造了n=2和n=3时具有SU(1,n)时空对称性的(2n-1)维自由费米子理论。这些理论在5维SU(1,3)不变理论中发挥作用,而这些理论被猜想能够完整描述某些6维超共形场论。我们找到了自由2n维玻色子-费米子系统的超对称性在(2n-1)维中的体现,并利用它来确定费米子两点函数。随后证明,完整的2n维两点函数可以通过重求和恢复。我们考虑了这些理论的极限,并观察到伽利略场论和卡罗尔场论出现在不同的区域中。我们确认了关联函数满足SU(1,n) Ward恒等式,并讨论了费米子在该群下的表示。

英文摘要:

We construct theories of free fermions in $(2n-1)$-dimensions with $SU(1,n)$ spacetime symmetry from the null reduction of fermions on a $2n$-dimensional $Ω$-deformed Minkowski background for $n=2$ and $n=3$. These play a role in the 5d $SU(1,3)$-invariant theories that are conjectured to offer a full description of certain 6d superconformal field theories. We find the $(2n-1)$-dimensional manifestation of the supersymmetry of a free $2n$-dimensional boson-fermion system, which we use to fix the fermion two-point functions. It is then shown that the full $2n$-dimensional two-point function can be recovered through resummation. Limits of the theories are considered, and it is observed that both Galilean and Carrollian field theories appear in different regimes. We confirm that the correlation functions obey the $SU(1,n)$ Ward identities and the representations of the fermions under this group are discussed.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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