标题： 对施瓦茨作用量的规范化 显示英文标题

标题： Gauging the Schwarzian Action

摘要： 在本工作中，我们将 Schwarzian 导数的全局$SL(2,\mathbb{R})$对称性提升为局部规范对称性。 为了实现这一点，我们开发了一种可能可以推广到$SL(2,\mathbb{R})$情况以外的程序：我们首先从基本场及其导数构造一个复合场，使其在群作用下线性变换。 然后我们写出其规范协变扩展并应用标准的规范技术。 将其应用于$SL(2,\mathbb{R})$的分式线性表示，我们得到 Schwarzian 导数的规范不变类比，作为复合场的协变导数的双线性不变量。 该框架使得与原始全局对称性相关的 Nöther 守恒荷的简单构造成为可能。 规范不变的 Schwarzian 作用量引入了$SL(2,\mathbb{R})$规范势，允许与额外场（如费米子）的局部不变耦合。 虽然这些势能在拓扑平凡区域上可以被规范掉，但非平凡拓扑（例如$S^1$）会导致不同的拓扑区。 我们提到，在二维引力的背景下，这些区可能对应于整体理论中之前讨论的缺陷。 显示英文摘要

摘要： In this work, we promote the global $SL(2,\mathbb{R})$ symmetry of the Schwarzian derivative to a local gauge symmetry. To achieve this, we develop a procedure that potentially can be generalized beyond the $SL(2,\mathbb{R})$ case: We first construct a composite field from the fundamental field and its derivative such that it transforms linearly under the group action. Then we write down its gauge-covariant extension and apply standard gauging techniques. Applying this to the fractional linear representation of $SL(2,\mathbb{R})$, we obtain the gauge-invariant analogue of the Schwarzian derivative as a bilinear invariant of covariant derivatives of the composite field. The framework enables a simple construction of N\"other charges associated with the original global symmetry. The gauge-invariant Schwarzian action introduces $SL(2,\mathbb{R})$ gauge potentials, allowing for locally invariant couplings to additional fields, such as fermions. While these potentials can be gauged away on topologically trivial domains, non-trivial topologies (e.g., $S^1$) lead to distinct topological sectors. We mention that in the context of two-dimensional gravity, these sectors could correspond to previously discussed defects in the bulk theory.