Speaker
Description
I will discuss the question posed in the title in the context of 2D CFTs. In particular, I will conjecture and provide some evidence that the answer is “always” if the two CFTs have the same left- and right-moving central charges, so long as one accepts topological interfaces of infinite quantum dimension. I will also illustrate how a topological interface between Theory A and Theory B allows one to transport knowledge about Theory A (its spectrum, its category of boundary conditions, its topological lines, etc.) to Theory B. Finally, I will explain some tiny miracles which make these ideas really come to life on the c=1 conformal manifold, and foreshadow a program wherein one completely solves c=1 conformal field theory in terms of the SU(2)1 WZW model. The talk is based on various projects with Yichul Choi and Ho Tat Lam, with Terry Gannon, and with Sven Möller.
