Cossu Guido, Del Debbio Luigi, Jüttner Andreas, Kitching-Morley Ben, Lee Joseph K L, Portelli Antonin, Rocha Henrique Bergallo, Skenderis Kostas
Braid Technologies, Shibuya 2-24-12, Tokyo, Japan.
Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom.
Phys Rev Lett. 2021 Jun 4;126(22):221601. doi: 10.1103/PhysRevLett.126.221601.
We present a study of the IR behavior of a three-dimensional superrenormalizable quantum field theory consisting of a scalar field in the adjoint of SU(N) with a φ^{4} interaction. A bare mass is required for the theory to be massless at the quantum level. In perturbation theory, the critical mass is ambiguous due to IR divergences, and we indeed find that at two loops in lattice perturbation theory the critical mass diverges logarithmically. It was conjectured long ago in [R. Jackiw et al., Phys. Rev. D 23, 2291 (1981)PRVDAQ0556-282110.1103/PhysRevD.23.2291, T. Appelquist et al., Phys. Rev. D 23, 2305 (1981)PRVDAQ0556-282110.1103/PhysRevD.23.2305] that superrenormalizable theories are nonperturbatively IR finite, with the coupling constant playing the role of an IR regulator. Using a combination of Markov Chain Monte Carlo simulations of the lattice-regularized theory, frequentist and Bayesian data analysis, and considerations of a corresponding effective theory, we gather evidence that this is indeed the case.
我们展示了一项关于三维超可重整化量子场论红外行为的研究，该理论由处于(SU(N))伴随表示的标量场与(\varphi^{4})相互作用组成。为使该理论在量子水平上无质量，需要一个裸质量。在微扰理论中，由于红外发散，临界质量是不明确的，并且我们确实发现在格点微扰理论的两圈阶，临界质量呈对数发散。早在[R. 杰基夫等人，《物理评论D》23，2291 (1981)PRVDAQ0556 - 282110.1103/PhysRevD.23.2291，T. 阿佩尔奎斯特等人，《物理评论D》23，2305 (1981)PRVDAQ0556 - 282110.1103/PhysRevD.23.2305]中就有人推测，超可重整化理论在非微扰情况下是红外有限的，耦合常数起到红外调节器的作用。通过结合格点正则化理论的马尔可夫链蒙特卡罗模拟、频率主义和贝叶斯数据分析以及对相应有效理论的考虑，我们收集到证据表明情况确实如此。
