论文标题
4d $ {\ cal n} = 1 $超符合字段理论的高速自旋超电流的三分函数
Three-point functions of higher-spin supercurrents in 4D ${\cal N}=1$ superconformal field theory
论文作者
论文摘要
我们开发了一种一般形式主义，以研究保守的高自旋超电流多重的三分相关函数$ j_ {α（r）\dotα（r）} $ in 4d $ {\ cal n} = 1 $ superConformal Theory。 $ {\ cal n} = 1 $超符号对称性$ \ langle j_ {α（r_1）\dotα（r_1）}用于任意$ r_1，r_2，r_3 $的派生，因此将问题主要减少到计算和组合。作为一个说明性的例子，我们明确地确定了$ \ langle j_ {α（r）\dotα（r）} J_ {β\dotβ} j_ {γ\dotγ} \ rangle $，其中$ j_ \dotα\dotα} $ s suppercrent。我们发现，这个三点函数取决于两个独立的张量结构，尽管相关器的精确形式取决于$ r $是偶数还是奇数。 CASE $ r = 1 $重现了Osborn派生的普通超级电流的三分函数。此外，我们提供了$ \ langle l l j_ {α（r）\dotα（r）} \ rangle $和$ \ langle j_ {α（r_1）\dotα（r_1）} j_______的$ _2 $ dot $ lange $ lange $ lange u_2 $ lange u_2 $ lange $ r_2 $ r_2 $ lange $ lange $ lange $ r_2当前多重。
We develop a general formalism to study the three-point correlation functions of conserved higher-spin supercurrent multiplets $J_{α(r) \dotα(r)}$ in 4D ${\cal N}=1$ superconformal theory. All the constraints imposed by ${\cal N}=1$ superconformal symmetry on the three-point function $\langle J_{α(r_1) \dotα(r_1)} J_{β(r_2) \dotβ(r_2) }J_{γ(r_3) \dotγ(r_3)}\rangle$ are systematically derived for arbitrary $r_1, r_2, r_3$, thus reducing the problem mostly to computational and combinatorial. As an illustrative example, we explicitly work out the allowed tensor structures contained in $\langle J_{α(r) \dotα(r)} J_{β\dotβ } J_{γ\dotγ}\rangle$, where $J_{α\dotα}$ is the supercurrent. We find that this three-point function depends on two independent tensor structures, though the precise form of the correlator depends on whether $r$ is even or odd. The case $r=1$ reproduces the three-point function of the ordinary supercurrent derived by Osborn. Additionally, we present the most general structure of mixed correlators of the form $\langle L L J_{α(r) \dotα(r)}\rangle$ and $\langle J_{α(r_1) \dotα(r_1)} J_{β(r_2) \dotβ(r_2)} L \rangle$, where $L$ is the flavour current multiplet.
