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，与其说是由于理论问题，不如说是由于缺乏清晰、明确的观测数据。目前的项目建议使用众所周知的观察，即基本物质成分是由手性费米子给出的，作为可能的量子引力场景的探针。手性对称是基本粒子物理学的一个重要组成部分。它保证了质量相对较小的费米子能够存在于自然界中。另一方面，手性可以被量子涨落自发地破坏，就像在电弱和强相互作用中的情况一样。由于引力预计会在普朗克尺度附近变得相关，引力波动一定不能破坏手性费米子的手性对称性。否则，在我们的宇宙中观测到的光费米子将与这种引力相互作用不相容。本提案的主要目的是将观测到的光（手性）费米子的存在与一般量子引力情景联系起来。为此，将使用已建立的量子场论理论框架，并将引力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：引力诱导的手性对称性破缺（引力催化）和费米子质量的产生在高能量子引力体系中是否活跃？手性对称性在引力催化作用下的突破是否会限制甚至排除某些量子引力场景？反过来，费米子场（例如，口味）的数量是否受到引力相互作用的限制？非手性费米子的存在与特定的量子引力场景兼容吗？这些问题的答案可能为量子引力理论的发展提供前所未有但严格的指导方针，量子引力理论不仅在数学上令人信服，而且与物理观测相一致。

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.