| Summary: | Abstract Drawing on insights from the Swampland program, we initiate a classification of infinite distance limits in the conformal manifolds of 4d SCFTs. Each limit is characterized by a Hagedorn-like behavior of the large N density of states, which we argue holographically correspond to different tensionless string limits. We focus on 4d large N SCFTs with simple gauge groups, which exhibit an overall free limit at infinite distance within the conformal manifold. In this class of theories, only three types of weak-coupling limits arise. They are distinguished by the exponential rate α of the anomalous dimension of the higher-spin tower, which we find to be determined by the ratio of the central charges a/c. We compute the large N partition function at the free point for all these SCFTs, and derive a universal expression for the Hagedorn temperature as a function of α (or, equivalently, of a/c), regardless of the gauge group or matter content. This Hagedorn-like density of states suggests that these weak-coupling limits correspond holographically to the tensionless limits of three different strings: the critical Type IIB string and two non-critical strings that arise exclusively in non-Einstein gravitational theories. Our findings are consistent with the Emergent String Conjecture when applied to theories with Einstein gravity at low energies. We also use our results to present a new argument for the absence of scale separation in the holographic AdS bulk dual of these 4d SCFTs. This argument is based on the existence of a bona fide ’t Hooft limit, or equivalently, on satisfying the sharpened lower bound for the Distance Conjecture.
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