近日，英国伦敦国王学院的Joseph Smith及其研究团队取得一项新进展。经过不懈努力，他们成功构造具有SU(1,n)时空对称性的费米子理论。相关研究成果已于2023年11月7日在国际知名学术期刊《高能物理杂志》上发表。

该研究团队基于n = 2和n = 3下Ω变形Minkowski背景2n维上费米子的零约化，成功构建了具备SU(1, n)时空对称性的(2n−1)维自由费米子理论。这一成果在5d SU(1,3)不变理论中发挥了重要作用，并被推测为能够提供某些6d超共形场论的完整描述。在研究过程中，研究人员发现了一个自由的2n维玻色子-费米子系统的超对称性的(2n−1)维表现形式，并利用它确定了费米子的两点函数。研究人员进一步通过重求和方法，成功恢复了完整的2n维两点函数。

除此之外，研究人员还深入探讨了理论的局限性，并观察到伽利略场论与卡罗场论在不同状态下的表现。最后，他们证实了相关函数服从SU(1, n) Ward恒等式，并就费米子在SU(1, n)群下的表示进行了讨论。

附：英文原文

Title: Fermions with SU(1, n) spacetime symmetry

Author: Smith, Joseph

Issue&Volume: 2023-11-07

Abstract: 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.

DOI: 10.1007/JHEP11(2023)032

Source: https://link.springer.com/article/10.1007/JHEP11(2023)032