三维超对称卡罗尔伽利略子
Supersymmetric Carroll Galileons in Three Dimensions
AI总结：
该研究提出首个含时空导数的相互作用卡罗尔超对称伽利略子类场论，通过推广二维伽利略/卡罗尔对偶至更高维并连接欧几里得超代数，构建相关多重态与张量微积分，为卡罗尔场论和超对称结构提供新见解。
摘要：
我们提出首个含时间与空间导数的相互作用卡罗尔超对称场论实例，其属于伽利略子类，非线性场方程的导数仍为二阶。为此，我们引入两种新工具：首先，通过在旋量基中表示生成元，证明二维伽利略/卡罗尔对偶可推广至更高维度且包含超对称性；其次，表明卡罗尔超代数自然连接欧几里得而非庞加莱超代数。利用三维N=1欧几里得超对称的实多重态，我们构建N=2卡罗尔超对称的标量多重态并发展张量微积分以实现上述模型。这些结果为真更高维卡罗尔场论与卡罗尔超对称的结构提供新见解，虽用于构建特定模型，但预期工具在卡罗尔物理学中具更广泛应用。
英文摘要：
We present the first example of an interacting Carroll supersymmetric field theory with both temporal and spatial derivatives, belonging to the Galileon class, where the non-linear field equation remains second-order in derivative. To achieve this, we introduce two novel tools. First, we demonstrate that the two-dimensional Galilei/Carroll duality can be extended to higher dimensions, and includes the supersymmetry, by expressing the generators in a spinor basis. We then show that Carroll superalgebras are naturally connected to Euclidean, rather than Poincaré, superalgebras. Using the real multiplet of the three-dimensional N $=1$ Euclidean supersymmetry, we construct the scalar multiplet for N $=2$ Carroll supersymmetry and develop a tensor calculus to realize the aforementioned model. These results offer new insights into the structure of genuine higher-dimensional Carroll field theories and Carroll supersymmetry. While these tools are utilized to build a specific model, we anticipate that they possess broader applications in Carrollian physics.
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