The CFT distance conjecture and tensionless string limits in $$ \mathcal{N} $$ = 2 quiver gauge theories

A bstract We initiate the study of infinite-distance limits on (complex) multi-dimensional conformal manifolds of 4d SCFTs and their bulk interpretation as tensionless-string limits in AdS/CFT. In particular, we focus on 4d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 SU quiver gauge theories with hypermultiplets in the bifundamental and fundamental representations. In the overall-free limit, we compute the large- N Hagedorn temperature T H , which governs the stringy exponential growth of the density of states at high energies. We argue that this quantity determines the type of stringy ultraviolet completion in the bulk: it captures the type of string theory in which the bulk physics is embedded while remaining insensitive to detailed geometric data. For linear quivers, we find that T H depends only on the quiver length, which is tied to the number of NS5-branes in the underlying brane construction and, in turn, to the string theory in which the bulk is embedded. For holographic quivers, where we impose that the two central charges a and c coincide in the large- N limit, we show that T H coincides with that of $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM, which befits the 10d Type IIB description of their gravitational duals. We also analyze the exponential rate α , which controls how the leading tower of higher-spin currents becomes conserved in these limits, as suggested by the CFT Distance Conjecture. In the large- N regime, we derive sharp bounds on the minimal rate, $$ 1/\sqrt{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msqrt> <mml:mn>2</mml:mn> </mml:msqrt> </mml:math> ≤ α min ≤ $$ \sqrt{2/3} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msqrt> </mml:math> , attained in the overall-free limit. Moreover, we prove that the universal lower bound α ≥ $$ 1/\sqrt{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msqrt> <mml:mn>2</mml:mn> </mml:msqrt> </mml:math> holds, including at finite N . Finally, we go beyond the overall-free ray by characterizing the convex hull of the $$ \overrightarrow{\alpha} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>α</mml:mi> <mml:mo>→</mml:mo> </mml:mover> </mml:math> -vectors that encode the exponential rate of the higher-spin towers along any (partial) weak-coupling limit.