Effective field theory for sub-MeV dark matter direct detection

对一类重要的有效场论（EFT）有了系统的了解，该理论与凝聚态系统相关，可以深入了解暗物质散射。具体来说，这些系统具有自发破缺的规范对称性。即使在研究较多的相对论情况下，也缺乏对这种EFT的系统处理。标准模型中的希格斯机制是一个经典的、可以说是最重要的例子。一个完整的和系统的理解，这是实现使用希尔伯特级数和散射振幅技术，反过来又从自发打破全球对称性理论的理解。这项工作纠正了一些关于希格斯有效场论的现有文献，希格斯有效场论在大型强子对撞机上被广泛用于研究希格斯扇区。一个有趣的可能性被确定和探索，即正在为探测器开发的有效场论也可以应用于暗物质本身。这被阐明，并发现一类光暗物质可以很好地理解使用EFT技术（并解决围绕星系和星系团观测中小尺度异常的一些谜团）。进一步发展了理解与凝聚态系统的大普适性类相关的EFT中量子效应的框架，并且发现了新的“非重整化”定理，该定理规定零是理论的所谓反常维数矩阵。

Developed a systematic understanding of an important class of effective field theories (EFTs), relevant for condensed matter systems that could provide insight into dark matter scattering. Specifically, these are systems that have spontaneously broken gauge symmetries. A systematic treatment of such EFTs was lacking, even in the more studied relativistic case. The classic and arguably most important example is the Higgs mechanism in the standard model. A complete and systematic understanding of this was achieved using Hilbert series and scattering amplitude techniques that were in turn developed from prior understanding of theories with spontaneously broken global symmetries. This work corrected some of the existing literature on the so-called Higgs Effective Field Theory, which is widely used at the large hadron collider to study the Higgs sector.An interesting possibility was identified and explored, that the effective field theory that was being developed for the detector could also be applied to the dark matter itself. This was elucidated, and found that a class of light dark matter could be well understood using EFT techniques (and resolve some mysteries surrounding small scale anomalies in galaxy and galaxy cluster observations).The framework for understanding quantum effects in EFTs that are relevant to a large universality class of condensed matter systems was further developed, and new 'non-renormalization' theorems which dictate zero is what is termed the anomalous dimension matrix of a theory were discovered.