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arXiv 2310.09698hep-th
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有效场论自举、大N $\chi$PT与全息QCD

Effective field theory bootstrap, large-N $χ$PT and holographic QCD

Yue-Zhou Li

AI总结:

本研究将有效场论自举表述为无限维半定规划,应用于大N手征微扰理论验证了对偶与原始方法的边界收敛性,结合幺正性约束证实大N展开自洽,并将其边界用于约束全息QCD的高阶导数修正。

摘要:

我们将有效场论(EFT)自举表述为一个由交叉对称求和规则与S矩阵原始假设构建的无限维半定规划(SDP),并对其展开综述。我们将该方案应用于研究大N手征微扰理论($\chi$PT),观察到对偶(排除型)与原始(纳入型)方法得到的EFT边界具有极佳的收敛性。这种收敛性与SDP中的对偶理论预测相符,使我们能够分析紫外(UV)能谱中的束缚态与共振态。此外,我们引入幺正性上界,通过原始方法从紫外标度$M$出发一致约束EFT空间,由此证实了大N展开的自洽性。最后,我们将大N $\chi$PT的边界转化为对全息QCD模型高阶导数修正的约束。

英文摘要:

We review the effective field theory (EFT) bootstrap by formulating it as an infinite-dimensional semidefinite program (SDP), built from the crossing symmetric sum rules and the S-matrix primal ansatz. We apply the program to study the large-$N$ chiral perturbation theory ($χ$PT) and observe excellent convergence of EFT bounds between the dual (rule-out) and primal (rule-in) methods. This convergence aligns with the predictions of duality theory in SDP, enabling us to analyze the bound states and resonances in the ultra-violet (UV) spectrum. Furthermore, we incorporate the upper bound of unitarity to uniformly constrain the EFT space from the UV scale $M$ using the primal method, thereby confirming the consistency of the large-$N$ expansion. In the end, we translate the large-$N$ $χ$PT bounds to constrain the higher derivative corrections of holographic QCD models.

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