The Hitchhiker's Guide to Tensionless String Limits in 4d SCFTs

Abstract

We study the appearance of universality classes in overall weak-coupling infinite-distance limits in the conformal manifold of 4d ${\cal N}=4,2,1$ superconformal gauge theories at large $N$ and their relation to the type of weakly-coupled emergent string in the AdS bulk dual using brane models. We focus on the complete set of theories with simple gauge group, and provide explicit Hanany-Witten constructions for each of them, including those that have non-Einstein bulk duals. This establishes that the three universality classes found in arXiv:2410.07309 are determined by the number of NS5-branes becoming coincident in a suitable double-scaling limit required to obtain the SCFT. Furthermore, all theories within a given universality class descend from the same parent theory by performing orbifold/orientifold projections (with possibly a small number of extra flavors), which are subleading effects at large $N$. This explains the origin of the universality classes from a CFT perspective. Moreover, we argue that theories in the same universality class share the same closed-string background -- generated by the double-scaled NS5-brane system -- in which the backreaction of D-branes is expected to generate the AdS throat holographically dual to the SCFT. We describe the corresponding worldsheet theories, and find that the three kinds of emergent tensionless strings correspond to the 10d type IIB string, a subcritical string previously studied in a related context, and a novel kind of string which we characterize in detail. Our tools are not limited to this set of SCFTs, but can be naturally applied to more general theories, and allow us to study interpolating models yielding a network of SCFTs related by partial weak-coupling limits. We explicitly discuss the generalization of our results to large classes of theories with more than one gauge factor and even to some quasi-conformal gauge theories.