Causality constraints in conformal field theory
Causality constraints in conformal field theory
复制标题
共形场论中的因果约束
DOI：
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发表时间：
2015
影响因子：
5.4
通讯作者：
Sandipan Kundu
中科院分区：
文献类型：
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作者：
Thomas Hartman;Sachin Jain;Sandipan Kundu
因果关系对Lorentz签名中的QFT施加了不平凡的约束，例如在低能量拉格朗日中固定某些项的符号。在d维共形场理论中，我们展示了这些约束是如何在欧几里德相关器的交叉对称性中编码的，并直接从共形自举(解析地)得到类似的约束。自举设置是一个洛伦兹四点函数，对应于通过冲击波的传播。交叉对称性修正了共形块展开中出现的某些对数项的符号，这限制了低位算符的相互作用。作为应用，我们用Bootstrap重新推导了有效场论中关于(∂ϕ)4耦合的符号约束。我们还发现了对具有较高自旋守恒流的理论的限制。我们的分析仅限于标量相关器，但我们认为，类似的方法也应该对自旋算符的相互作用施加不平凡的限制。
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂ϕ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.