标题： 非相对论共形场论中的大电荷展开 显示英文标题

标题： The large-charge expansion in nonrelativistic conformal field theories

摘要： 共形场论（CFTs）与临界现象和相变有关，同时在弦理论中也扮演着至关重要的角色。由于共形不变性，求解一个CFT是一个极其受限的问题——本质上归结为计算一组称为CFT数据的数字——但它仍然非常非平凡。事实上，CFTs通常是强耦合的，因此需要新的工具，这些工具不依赖微扰论。出于这些原因，在过去几十年里，它们成为最活跃的研究领域之一。 这些思想的一个自然扩展，对于相对论效应不明显的凝聚态系统具有深远意义，就是用伽利略群代替庞加莱群，从而为用非相对论共形场论（NRCFTs）精确描述整个新类别的临界现象开辟了道路。 然后，许多上述用于更好地理解CFTs的工具可以被改编，以在具有直接实验相关性的系统中获得强大的预测能力。 近年来，一种新的强大工具出现了：大电荷展开。它允许系统地揭示具有全局对称性的理论的部分CFT数据，从而揭示这些系统的深刻和普遍特征。利用态算符对应关系，大多数计算进一步简化为评估由大电荷有效场论描述的有限密度系统中的能级，通常与共形超流体相相关。 然而，非相对论情况下的大电荷动力学比其相对论对应物更丰富——因此，更具挑战性。在这篇论文中，我们讨论了最近取得的进展，这些进展开启了众多令人兴奋的大电荷应用的大门。 显示英文摘要

摘要： Conformal field theories (CFTs) are associated with critical phenomena and phase transitions and also play an essential role in string theory. Solving a CFT is an extremely constrained problem due to conformal invariance -- the task essentially reduces to the computation of a set of numbers called the CFT data -- yet it remains highly nontrivial. In fact, CFTs usually are strongly coupled and thus require new tools that do not rely on perturbation theory. For these reasons, in the past few decades, they became one of the most active fields of research. A natural extension of these ideas with far-reaching implications for condensed matter systems -- in which relativistic effects are not manifest -- is to replace the Poincare group by the Galilean group, thereby opening the way to a precise formulation of a whole new class of critical phenomena in terms of nonrelativistic conformal field theories (NRCFTs). Many of the aforementioned tools developed to gain a better formal understanding of CFTs can then be adapted to gain a strong predictive power in systems with direct experimental relevance. In recent years, a new powerful tool has emerged: the large-charge expansion. It allows to systemically uncover part of the CFT data of theories with global symmetries, thereby revealing profound and universal features of these systems. Using the state-operator correspondence, most of the computations are further reduced to the evaluation of energy levels in a finite-density system described by a large-charge effective field theory, usually associated with a conformal superfluid phase. The large-charge dynamics in the nonrelativistic case is however richer -- and therefore, more challenging -- than its relativistic counterpart. In this thesis, we discuss recent progress which opened the door to many new exciting large-charge applications.