标题： 量子理论中与规范场耦合的运行耦合常数 显示英文标题

标题： Running Couplings in Quantum Theory of Gravity Coupled with Gauge Fields

摘要： 在本文中，我们研究了非阿贝尔规范场与高阶导数引力的耦合系统。在该耦合系统中研究了电荷重整化。发现规范耦合常数的β函数中的主要项是由于规范场与引力子的相互作用产生的。这被证明是一个普遍量，因为它不依赖于规范耦合和规范群，但可能依赖于作用量中的其他耦合（引力和物质）。在单环情况下研究了该耦合系统。发现四维空间中规范β函数的主要项在单环下为零。研究了规范场对引力耦合常数演化的影响。显示当考虑量子修正时，规范场与高阶导数引力的耦合系统满足单位性。此外，发现牛顿常数在短距离下趋于零。在这个规范场与高阶导数引力耦合的可重整化且满足单位性的理论中，对于所有规范群都发现规范β函数的主要项是普遍的，并通过在四维空间中与引力耦合的阿贝尔规范理论的上下文中将其隔离，进一步详细研究了该主要项。利用四维空间中阿贝尔规范理论的自对偶性，显示该规范β函数的该项在所有环中都为零。发现该结果与引力作用量、正则化方案和规范固定条件无关。对任意引力作用量的显式单环计算进一步证明了在四维空间中该规范β函数的该项为零，与正则化方案和规范固定条件无关。讨论了这些结果的后果。 显示英文摘要

摘要： In this paper we study the coupled system of non-abelian gauge fields with higher-derivative gravity. Charge renormalization is investigated in this coupled system. It is found that the leading term in the gauge coupling beta function comes due to interaction of gauge fields with gravitons. This is shown to be a universal quantity in the sense that it doesn't depend on the gauge coupling and the gauge group, but may depend on the other couplings of the action (gravitational and matter). The coupled system is studied at one-loop. It is found that the leading term of gauge beta function is zero at one-loop in four dimensions. The effect of gauge fields on the running of gravitational couplings is investigated. The coupled system of gauge field with higher-derivative gravity is shown to satisfy unitarity when quantum corrections are taken in to account. Moreover, it is found that Newton constant goes to zero at short distances. In this renormalizable and unitary theory of gauge field coupled with higher-derivative gravity, the leading term of the gauge beta function, found to be universal for all gauge groups, is further studied in more detail by isolating it in the context of abelian gauge theories coupled with gravity in four dimensions. Using self-duality of abelian gauge theories in four dimensions, this term of the gauge beta function is shown to be zero to all loops. This is found to be independent of the gravity action, regularization scheme and gauge fixing condition. An explicit one-loop computation for arbitrary gravity action further demonstrates the vanishing of this term in the gauge beta function in four dimensions, independent of the regularization scheme and gauge fixing condition. Consequences of this are discussed.