The CFT Distance Conjecture and Tensionless String Limits in $\mathcal N=2$ Quiver Gauge Theories

TL;DR

This work extends the CFT Distance Conjecture to four-dimensional N=2 quiver gauge theories with multifaceted conformal manifolds, linking infinite-distance limits to tensionless-string regimes in AdS/CFT. It shows that the large-N Hagedorn temperature T_H serves as a coarse diagnostic of the bulk UV completion, with a striking universality for linear quivers where T_H depends only on the quiver length p, and with holographic quivers (a ≈ c) yielding T_H equal to that of N=4 SYM, consistent with a 10d Type IIB bulk dual. The authors also develop a convex-hull framework for the HS towers via α-vectors, deriving sharp bounds α_min ∈ [1/√2, √(2/3)] in the large-N limit and proving the universal lower bound α ≥ 1/√2 at finite N. They show that the α–T_H correspondence can fail for non-holographic cases due to contributions from multiple sectors in AdS, while holographic theories realize a cleaner one-to-one relation as extended objects decouple from the AdS scale. Collectively, these results illuminate how conformal-manifold geometry, HS towers, and bulk string UV completions interrelate in AdS/CFT, and they suggest rich future directions in class S theories, brane realizations, and taxonomy of asymptotic regimes.

Abstract

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 $\mathcal{N}=2$ $SU$ 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 $\mathcal{N}=4$ 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, $1/\sqrt{2}\le α_{\min}\le \sqrt{2/3}$, attained in the overall-free limit. Moreover, we prove that the universal lower bound $α\ge 1/\sqrt{2}$ holds, including at finite $N$. Finally, we go beyond the overall-free ray by characterizing the convex hull of the $\vecα$-vectors that encode the exponential rate of the higher-spin towers along any (partial) weak-coupling limit.

Figures (6)

• Figure 1: A linear quiver with fundamental flavor multiplets.
• Figure 2: The Hanany--Witten setup. The black lines denote NS5-branes, the blue lines represent a stack of $N_i$ D4-branes, and the green dots represent a stack of $K_i$ D6-branes.
• Figure 3: Convex hulls for the weakly-coupled frames of the $SU(N)\times SU(N)$ circular quiver (left), $SU(N)\times SU(N)$ linear quiver (middle), and $SU(N)\times SU(2N)$ circular quiver (right) at large $N$. The grey arrow depicts the unit normal vector $\hat{n}$ that points towards the overall-free limit. The curved blue line is the boundary of the ball of radius $1/\sqrt{2}$. The fact that the convex hull contains this ball shows that the bound $\alpha \geq 1/\sqrt{2}$ is satisfied Calderon-Infante:2020dhm.
• Figure 4: A quiver of type $D$.
• Figure 5: Applying the Schur complement formula.