Chiral Fermions and Quantum Gravity

发展一个令人信服和一致的量子引力理论的挑战，与其说是受到理论问题的阻碍，不如说是因为缺乏明确的观测数据。本项目建议使用基本物质成分由手征费米子给出的著名观测作为可能的量子引力情景的探测器。手征对称性是基本粒子物理中的一个基本要素。它确保了质量相对较小的费米子可以在自然界中存在。另一方面，手性可以被量子涨落自发破坏，就像弱电相互作用和强相互作用一样。由于引力有望在普朗克尺度附近变得相关，重力波动不能破坏手征费米子的手征对称性。否则，在我们的宇宙中观测光费米子将与这种引力相互作用不相容。这个提议的主要目标是将所观察到的光(手性)费米子的存在与一般的量子引力情景联系起来。为此，建立的量子场论的理论框架将被用于引力被视为有效场论或渐近安全的基本量子理论。有了这个工具，该项目可以解决以下问题：在高能量子引力区域，引力诱导的手性对称破缺(引力催化)和费米子质量产生能否活跃？突破引力催化的手征对称性会限制甚至排除某些量子引力情景吗？反过来，费米子场的数量(例如，味道)是否受引力相互作用的限制？非手征费米子的存在是否与特定的量子引力场景兼容？这些问题的答案可能会为量子引力理论的发展提供前所未有但严格的指导方针，这种理论不仅在数学上令人信服，而且与物理观测兼容。

The challenge of developing a convincing and consistent theory of quantum gravity is hampered perhaps less by theoretical problems than by the lack of clear observational unambiguous data. The present project suggests to use the well-known observation that the fundamental matter constituents are given by chiral fermions as a probe for possible quantum gravity scenarios.Chiral symmetry is an essential ingredient in elementary particle physics. It ensures that fermions with comparatively small masses can exist in Nature. On the other hand, chirality can be spontaneously broken by quantum fluctuations, as it is the case in the electroweak and strong interactions. As gravity are expected to become relevant near the Planck scale, gravity fluctuations must not break the chiral symmetry of the chiral fermions. Otherwise the observation of light fermions in our universe would not be compatible with such gravity interactions.The main objective of this proposal is to interconnect the observed existence of light (chiral) fermions with generic quantum gravity scenarios. For this, the established theoretical framework of quantum field theory will be used with gravity being treated either as an effective field theory or an asymptotically safe fundamental quantum theory. With this tool the project can address the following questions: Can gravitationally induced chiral symmetry breaking (gravitational catalysis) and fermion mass generation be active in the high-energy quantum gravity regime? Does chiral symmetry breaking through gravitational catalysis put constraints on or even rule out some quantum-gravity scenarios? In turn, is the number of fermion fields (e.g., flavors) constrained through gravitational interactions? Is the existence of non-chiral fermions compatible with specific quantum gravity scenarios? Answers to these questions may provide unprecedented but stringent guidelines to the development to a quantum gravity theory that is not only mathematically convincing but also compatible with physical observations.