Seed conformal blocks in 4D CFT
Seed conformal blocks in 4D CFT
复制标题
在 4D CFT 中种子保形块
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
M. Serone
中科院分区：
文献类型：
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作者：
A. Echeverri;Emtinan Elkhidir;D. Karateev;M. Serone
本文用封闭的解析形式计算了四维共形场论中Lorentz群的任意表示（？，？$$ overline{ell} $$）中一般混合对称旋量/张量算符交换所涉及的“种子”共形块的最小集合.这些块产生于涉及两个标量的4点函数，一个（0，|−|）和（|−|，0）旋量或张量。我们直接解决了卡西米尔方程组，可以优雅地写在任何（，$$ overline{ell} $$）的紧凑形式，通过使用受过教育的Anastrophic和减少问题的代数线性系统。各种细节上的形式，已推导出的形式的反，通过使用所谓的阴影形式主义。共形块的复杂性取决于p =| −|并且随着p而增长，类似于当d增加时d偶数时空维度中的标量共形块所发生的情况。这些结果为在四维共形场论中引导涉及任意旋量/张量算子的4点函数开辟了道路。
A bstractWe compute in closed analytical form the minimal set of “seed” conformal blocks associated to the exchange of generic mixed symmetry spinor/tensor operators in an arbitrary representation (ℓ, ℓ¯$$ overline{ell} $$) of the Lorentz group in four dimensional conformal field theories. These blocks arise from 4-point functions involving two scalars, one (0, |ℓ − ℓ¯$$ overline{ell} $$|) and one (|ℓ − ℓ¯$$ overline{ell} $$|, 0) spinors or tensors. We directly solve the set of Casimir equations, that can elegantly be written in a compact form for any (ℓ, ℓ¯$$ overline{ell} $$), by using an educated ansatz and reducing the problem to an algebraic linear system. Various details on the form of the ansatz have been deduced by using the so called shadow formalism. The complexity of the conformal blocks depends on the value of p = |ℓ − ℓ¯$$ overline{ell} $$| and grows with p, in analogy to what happens to scalar conformal blocks in d even space-time dimensions as d increases. These results open the way to bootstrap 4-point functions involving arbitrary spinor/tensor operators in four dimensional conformal field theories.