从二维树级弹性过程得到单圈非弹性振幅
One-loop inelastic amplitudes from tree-level elasticity in 2d
AI总结：
本文研究1+1维量子场论的单圈微扰可积性，给出由树级弹性振幅构造任意外部腿单圈非弹性振幅的公式，并证明单连通仿射Toda理论可通过整体缩放势恢复可积性。
摘要：
我们研究了1+1维中不同量子场论在单圈阶的微扰可积性。从具有类多项式势且在树级不存在非弹性过程的有质量玻色子拉格朗日量出发，我们推导了一个公式，可重现任意外部腿数的单圈非弹性振幅。我们证明，任何单圈非弹性振幅都等于其树级形式，其中粒子和传播子的质量由单圈泡泡图给出修正。这些振幅通常非零，因此需要向拉格朗日量添加反项，以在单圈阶恢复可积性。对于单连通仿射Toda理论这一类别，我们证明所需反项可通过用一个整体乘法因子缩放势来获得，从而证明了这些模型的单圈可积性。尽管我们关注具有类多项式相互作用的玻色子理论，但我们预期本文用于计算振幅的在壳技术可应用于其他若干模型。
英文摘要：
We investigate the perturbative integrability of different quantum field theories in 1+1 dimensions at one loop. Starting from massive bosonic Lagrangians with polynomial-like potentials and absence of inelastic processes at the tree level, we derive a formula reproducing one-loop inelastic amplitudes for arbitrary numbers of external legs. We show that any one-loop inelastic amplitude is equal to its tree-level version, in which the masses of particles and propagators are corrected by one-loop bubble diagrams. These amplitudes are nonzero in general and counterterms need to be added to the Lagrangian to restore the integrability at one loop. For the class of simply-laced affine Toda theories, we show that the necessary counterterms are obtained by scaling the potential with an overall multiplicative factor, proving in this way the one-loop integrability of these models. Even though we focus on bosonic theories with polynomial-like interactions, we expect that the on-shell techniques used in this paper to compute amplitudes can be applied to several other models.
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