We reconsider some older constructions of T-duality, based on automorphisms of the worldsheet operator algebra, in a modern context. It has been long known that at special points in the moduli space of torus compactifications, the target space gauge symmetry may be enhanced. Away from such points the symmetry is broken and T-duality may be understood as a residual discrete gauge symmetry that survives this breaking. Drawing on work on connections over the space of string backgrounds, we discuss how to generalise this framework for T-duality to geometric and non-geometric backgrounds that are not full solutions of string theory, but may play an important role in exact backgrounds. Along the way we find an interesting algebraic structure and discuss its relationship with doubled geometry. We comment on non-isometric T-duality in this context.

在现代环境下，我们基于worldsheet运算符代数的自同构性，重新考虑了T-对偶的一些较早的构造。众所周知，在圆环压实的模量空间中的特定点处，可以提高目标空间规的对称性。远离这样的点，对称性被破坏，并且T对偶性可以理解为在该破坏中幸存的残余离散量规对称性。利用字符串背景空间上的连接方面的工作，我们讨论如何将T-对偶性框架推广到不是字符串理论的完整解决方案但可以在确切背景中发挥重要作用的几何和非几何背景。一路上，我们找到了一个有趣的代数结构，并讨论了它与成对几何的关系。我们在这种情况下评论非等距的T对偶。