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arXiv 2106.04604hep-th
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AdS中的穿戴与共形Bethe-Salpeter方程

Dressing in AdS and a Conformal Bethe-Salpeter Equation

Sylvain Fichet

备注：
v2: 7+6 pages, 4 figures, minor edits, supplemental material included, matches journal version
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AI总结：

该研究在AdS中研究微扰QFT的Dyson方程，揭示穿戴传播子导致OPE修正和1/N效应重求和，并推导出共形Bethe-Salpeter方程，发现带1/N^2结合能的束缚态。

摘要：

我们启动了AdS中微扰QFT的Dyson方程及其对大N CFT影响的研究。我们展示了穿戴的单粒子AdS传播子具有波函数重整化和算子混合，从而对OPE数据产生有限修正。我们展示了CFT中1/N效应的重求和如何从AdS中的穿戴中涌现。当边界到体传播子被共形维数之和低于主维数的传播子穿戴时，它无法映射到CFT源；我们将此与粒子不稳定性的AdS/CFT版本联系起来。我们研究了两粒子传播子的穿戴，并获得了“束缚态”算子共形部分波的共形Bethe-Salpeter方程。我们为梯子核的情况提供了自包含的计算。我们展示了共形维数等于其组成维数之和加上1/N^2抑制的“结合能”的束缚态的出现。Dyson方程的重求和对于推导这些结果是必不可少的。

英文摘要：

We initiate the study of Dyson equations of perturbative QFT in AdS and their consequences for large-N CFT. We show that the dressed one-particle AdS propagator features wavefunction renormalization and operator mixing, giving rise to finite corrections to OPE data. We show how the resummation of 1/N effects in the CFT emerges from the dressing in AdS. When a boundary-to-bulk propagator is dressed by propagators whose sum of conformal dimensions is lower than the main dimension, it cannot map onto a CFT source; we relate this to an AdS/CFT version of particle instability. We investigate the dressing of the two-particle propagator and obtain a conformal Bethe-Salpeter equation for the conformal partial wave of a "bound state" operator. We provide a self-contained calculation for the case of a ladder kernel. We show that a bound state with conformal dimension equal to the sum of its constituents plus a 1/N^2-suppressed "binding energy" emerges. Resummation of the Dyson equations is essential for deriving these results.

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