On the quadratic equations for detecting duality symmetries of c=2 compact boson CFTs

Recently, a lot of researchers have explored generalized symmetries of many kinds of quantum field theories. Among them, we will talk about how to construct some families of duality symmetries of some conformal field theories (CFT), known as the categorical symmetries built by using the T-duality and half-space gauging. The kind of CFTs we will focus on is compact boson CFT with the central charge 2, considering taking orbifold (gauging) of diagonal subgroups of U(1). In this set up, we find quadratic equations whose solutions correspond to duality defects, which implies that we can explore the duality symmetries of such CFTs finding solutions of the equations. We will also talk about some brief example of defects that can be found by the equations. This is based on arXiv:2412.01319.