In this talk, I will discuss various aspects of the Distance Conjecture in AdS/CFT. First, I will briefly introduce the Distance Conjecture and how to naturally translate it to the CFT side, as encoded in the CFT Distance Conjecture. In the second part, I will sketch a proof of the first statement in this conjecture, namely that higher-spin symmetry always lies at infinite distance in the conformal manifold of any local CFT in more than two dimensions. For the third part, we will change gears from model-independent proofs to asking more refined questions in well-known models. Specifically, we will focus on a mini-landscape of supersymmetric CFTs in four dimensions which feature three distinct infinite distance limits distinguished by the CFT Distance Conjecture parameter. Borrowing insights from the Swampland program, I will argue that these three limits correspond to three different strings becoming tensionless in AdS. To support this claim, I will discuss how some properties of these CFTs, such as their large N Hagedorn temperature, are determined solely by the CFT Distance Conjecture parameter. I will also discuss how one of these limits nicely fits with the Type IIB string, while another corresponds to a non-critical string theory in AdS.
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Julio Parra-Martinez & Xinliang Lyu
