标题： 尺度对称性破缺与量子临界点处质量的产生 显示英文标题

标题： Scale Symmetry Breaking and Generation of Mass at Quantum Critical Points

摘要： 我们研究了一个渐近自由的理论，其中包含$N$个相对论狄拉克费米子和一个实标量场，在三维空间中通过杨-米尔斯相互作用和标量自相互作用进行耦合，使用了功能重整化方法。 在费米子味数很多的极限下，由于量子涨落，三阶标量耦合变得恰好是边缘的，导致了一条强耦合的红外固定点线。 即使没有手征对称性，也可以通过量子相变生成费米子质量。 由于真空稳定性的丧失，固定点线在临界端点终止。 正好在端点处，尺度对称性被自发打破，导致费米子质量的生成。 有趣的是，手征对称性的缺失是费米子质量自发生成的前提，而不是其结果。 我们还强调了在临界点及非临界点处格罗斯-内沃理论和格罗斯-内沃-杨-米尔斯理论之间的密切相似性，并确立了它们的功能RG流和量子有效作用在大$N$下的等价性。 进一步的影响，包括对共形场理论的影响，也被指出。 显示英文摘要

摘要： We study an asymptotically free theory of $N$ relativistic Dirac fermions and a real scalar field coupled by Yukawa and scalar self-interactions in three dimensions using functional renormalisation. In the limit of many fermion flavours, the cubic scalar coupling becomes exactly marginal due to quantum fluctuations, leading to a line of strongly-coupled infrared fixed points. Fermion mass can be generated through a quantum phase transition even if chiral symmetry is absent. The line of fixed points terminates at a critical endpoint due to the loss of vacuum stability. Exactly at the endpoint, scale symmetry is broken spontaneously, leading to the generation of fermion mass. Intriguingly, the absence of chiral symmetry is a prerequisite for the spontaneous generation of fermion mass, and not a consequence thereof. We also highlight close similarities between Gross-Neveu and Gross-Neveu--Yukawa theories at and away from critical points, and establish the large-$N$ equivalence of their functional RG flows and quantum effective actions. Further implications including for conformal field theories are indicated.