Classical and Quantum Gravity ( IF 3.5 ) Pub Date : 2021-08-12 , DOI: 10.1088/1361-6382/ac161b Marco Frasca 1 , Anish Ghoshal 2
We investigate the non-perturbative degrees of freedom (d.o.f.) in the class of non-local Higgs theories that have been proposed as an ultraviolet completion 4D quantum field theory generalizing the kinetic energy operators to an infinite series of higher derivatives inspired by string field theory and ghost-free non-local approaches to quantum gravity. At the perturbative level, the d.o.f. of non-local Higgs are the same of the local theory. We prove that, at the non-perturbative level, the physical spectrum of the strongly-coupled Higgs mass is actually corrected from the ‘infinite number of derivatives’ present in the action. The technique we use permits to derive the set of Dyson–Schwinger equations in differential form. This proves essentially useful when exact solutions to the local equations are known. We show that all the formalism of the local theory involving the Dyson–Schwinger approach extends quite naturally to the non-local case. Using these methods, the spectrum of the strongly-coupled non-local theories become accessible in the non-perturbative regimes. We calculate the N-point correlation functions and predict the mass-gap in the spectrum arising purely from the self-interaction and the non-local scale M. The proper weak perturbation limit is correctly recovered from the strong coupling regime in the limit of the coupling of the theory goes to zero. Our results show the mass gap generated in the non-local theories gets damped in the UV and it reaches conformal limit. We discuss the implications of our result in particle physics and cosmology.
中文翻译:
强耦合无限导数非局域希格斯粒子中的质量间隙:戴森-施温格方法
我们研究了非局部希格斯理论类中的非微扰自由度 (dof),这些理论已被提出作为紫外线完成 4D 量子场理论,将动能算符推广到受弦场理论启发的无限系列更高导数量子引力的无鬼非局域方法。在微扰水平上,非局域希格斯粒子的自由度与局域理论相同。我们证明,在非微扰水平上,强耦合希格斯质量的物理光谱实际上是从作用中存在的“无限数量的导数”中校正的。我们使用的技术允许以微分形式推导出 Dyson-Schwinger 方程组。当局部方程的精确解已知时,这证明是非常有用的。我们表明,涉及戴森-施温格方法的局部理论的所有形式主义很自然地扩展到非局部情况。使用这些方法,强耦合非局部理论的频谱在非微扰机制中变得可用。我们计算N点相关函数并预测光谱中完全由自相互作用和非局部尺度M产生的质量间隙。在理论耦合的极限趋于零的情况下,从强耦合状态正确恢复了适当的弱扰动极限。我们的结果表明,非局域理论中产生的质量间隙在 UV 中受到阻尼并达到共形极限。我们讨论了我们的结果对粒子物理学和宇宙学的影响。