标题： 拓扑场理论中的Higgs转换与Chern-Simons物质理论中的非可逆对称性 显示英文标题

标题： Higgsing Transitions from Topological Field Theory & Non-Invertible Symmetry in Chern-Simons Matter Theories

摘要： 非可逆的一阶对称性在(2+1)d拓扑量子场论中自然实现。 在本工作中，我们考虑这种对称性在(2+1)d共形场论中的潜在实现，研究无能隙系统是否可以表现出类似的对称结构。 为此，我们讨论了由Chern-Simons物质理论中的Higgs机制驱动的(2+1)d拓扑场论之间的转变。 这种转变可以通过用晶格状域墙网络填充时空来宏观建模，该网络分隔两个拓扑相。 在域墙上是描述由局部消失的标量质量束缚的无能隙手征模式的商共形场论。 在本次演讲中，可以通过使用任意子凝聚来跟踪域墙网络中的线，从而推导出转变点的一阶对称性。 利用这个框架，我们讨论了固定点理论中非可逆一阶对称性的各种具体例子。 例如，$SU(k)_{2}$陈-西蒙斯理论与对称张量表示中的标量耦合会产生从$SU(k)_{2}$相到$SO(k)_{4}$相的转变，并在固定点具有非可逆一阶对称性$PSU(2)_{-k}$。 我们还讨论了具有$Spin(2N)$和$E_{7}$规范群的理论，这些理论表现出其他非可逆一阶对称性的模式。 在我们许多例子中，非可逆一阶对称性本身并不是一个模不变的拓扑量子场论，因此是固定点动力学的固有部分。 显示英文摘要

摘要： Non-invertible one-form symmetries are naturally realized in (2+1)d topological quantum field theories. In this work, we consider the potential realization of such symmetries in (2+1)d conformal field theories, investigating whether gapless systems can exhibit similar symmetry structures. To that end, we discuss transitions between topological field theories in (2+1)d which are driven by the Higgs mechanism in Chern-Simons matter theories. Such transitions can be modeled mesoscopically by filling spacetime with a lattice-shaped domain wall network separating the two topological phases. Along the domain walls are coset conformal field theories describing gapless chiral modes trapped by a locally vanishing scalar mass. In this presentation, the one-form symmetries of the transition point can be deduced by using anyon condensation to track lines through the domain wall network. Using this framework, we discuss a variety of concrete examples of non-invertible one-form symmetry in fixed-point theories. For instance, $SU(k)_{2}$ Chern-Simons theory coupled to a scalar in the symmetric tensor representation produces a transition from an $SU(k)_{2}$ phase to an $SO(k)_{4}$ phase and has non-invertible one-form symmetry $PSU(2)_{-k}$ at the fixed point. We also discuss theories with $Spin(2N)$ and $E_{7}$ gauge groups manifesting other patterns of non-invertible one-form symmetry. In many of our examples, the non-invertible one-form symmetry is not a modular invariant TQFT on its own and thus is an intrinsic part of the fixed-point dynamics.