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Background Independence in Gauge Theories
Annales Henri Poincaré ( IF 1.5 ) Pub Date : 2020-02-03 , DOI: 10.1007/s00023-020-00887-4
Mojtaba Taslimi Tehrani , Jochen Zahn

Classical field theory is insensitive to the split of the field into a background configuration and a dynamical perturbation. In gauge theories, the situation is complicated by the fact that a covariant (w.r.t. the background field) gauge fixing breaks this split independence of the action. Nevertheless, background independence is preserved on the observables, as defined via the BRST formalism, since the violation term is BRST exact. In quantized gauge theories, however, BRST exactness of the violation term is not sufficient to guarantee background independence, due to potential anomalies. We define background-independent observables in a geometrical formulation as flat sections of the observable algebra bundle over the manifold of background configurations, with respect to a flat connection which implements background variations. A theory is then called background independent if such a flat (Fedosov) connection exists. We analyze the obstructions to preserve background independence at the quantum level for pure Yang–Mills theory and for perturbative gravity. We find that in the former case, all potential obstructions can be removed by finite renormalization. In the latter case, as a consequence of power-counting non-renormalizability, there are infinitely many non-trivial potential obstructions to background independence. We leave open the question whether these obstructions actually occur.

中文翻译:

规范理论的背景独立性

古典场论对将场划分为背景结构和动态扰动不敏感。在规范理论中,由于协变量(破坏了背景场)的规范破坏了动作的这种分裂独立性,因此情况变得复杂。但是,由于违反项是BRST精确的,因此根据BRST形式主义的定义,可观察对象保留了背景独立性。但是,在量化规范理论中,由于潜在的异常,违反条款的BRST准确性不足以保证背景独立性。我们相对于实现背景变化的平面连接,以几何形式将与背景无关的可观察物定义为可观察的代数束的平坦部分,这些可观察的代数束位于背景构造的流形上。如果存在这种平坦的(Fedosov)连接,则将一种理论称为独立于背景的理论。我们分析了纯Yang-Mills理论和微扰引力在量子水平上保持背景独立性的障碍。我们发现,在前一种情况下,所有潜在的障碍都可以通过有限的重新规范化来消除。在后一种情况下,由于对不可重归一性进行功率计数,结果对背景独立性存在无数潜在的重要影响。我们悬而未决的问题是这些障碍是否真的发生了。可以通过有限的重新归一化来消除所有潜在的障碍。在后一种情况下,由于对不可重归一化进行了功率计数,因此对背景独立性存在无数潜在的重要影响。我们悬而未决的问题是这些障碍是否真正发生。可以通过有限的重新归一化来消除所有潜在的障碍。在后一种情况下,由于对不可重归一性进行功率计数,结果对背景独立性存在无数潜在的重要影响。我们悬而未决的问题是这些障碍是否真的发生了。
更新日期:2020-02-03
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