In the first part of this talk, I will introduce the CFT Distance Conjecture as the AdS/CFT dual of the Swampland Distance Conjecture. Then, I will discuss a proof for its first part, which states that higher-spin symmetry must always lie at infinite distance in the conformal manifold of any local CFT in more than two dimensions. In the second part, I will address the stringy origin of these higher-spin symmetries. Focusing on 4d SCFTs, I will give several arguments suggesting the existence of two new strings in AdS, apart from the usual 10d critical superstring. Along the way, we will find a remarkable connection between no scale separation and the Sharpened Distance Conjecture.

CERN