Conformal Quivers and Melting Molecules

TL;DR

This work builds a bridge between quiver quantum mechanics and AdS2 physics by deriving the Coulomb-branch dynamics of a three-node Abelian quiver and uncovering a scaling regime with emergent $SL(2,\mathbb{R})$ conformal symmetry. It shows that, on the scaling throat, the Coulomb branch behaves as a multi-particle conformal quantum mechanical system with velocity-dependent forces, and it demonstrates how finite-temperature effects melt the Coulomb branch into the Higgs branch, mirroring gravitational intuitions about thermally driven collapse. The paper also analyzes wavefunctions and SUSY structure within the scaling theory, and discusses holographic implications, random-matrix perspectives, and potential extensions, including higher-node quivers and superpotential corrections. Overall, it provides a concrete, tractable model for exploring AdS2/CQM-like dynamics and the thermal fate of scaling microstates in black hole physics.

Abstract

Quiver quantum mechanics describes the low energy dynamics of a system of wrapped D-branes. It captures several aspects of single and multicentered BPS black hole geometries in four-dimensional $\mathcal{N} = 2$ supergravity such as the presence of bound states and an exponential growth of microstates. The Coulomb branch of an Abelian three node quiver is obtained by integrating out the massive strings connecting the D-particles. It allows for a scaling regime corresponding to a deep AdS$_2$ throat on the gravity side. In this scaling regime, the Coulomb branch is shown to be an $SL(2,\mathbb{R})$ invariant multi-particle superconformal quantum mechanics. Finally, we integrate out the strings at finite temperature---rather than in their ground state---and show how the Coulomb branch `melts' into the Higgs branch at high enough temperatures. For scaling solutions the melting occurs for arbitrarily small temperatures, whereas bound states can be metastable and thus long lived. Throughout the paper, we discuss how far the analogy between the quiver model and the gravity picture, particularly within the AdS$_2$ throat, can be taken.

Figures (16)

• Figure 1: A 3-node quiver diagram which captures the field content of the Lagrangian $L=L_V+L_C+L_W$, each piece of which is given in (\ref{['quiverqm']}), (\ref{['quiverqm2']}), and (\ref{['quiverqm3']}). This quiver admits a closed loop if $\kappa^1$, $\kappa^2>0$ and $\kappa^3<0$.
• Figure 2: Examples of $H+a\,K$ eigenfunctions. Left: Plot of $\widetilde{\psi}_\lambda(x)$ for $n \in (0.2,5.2)$ in unit increments. Right: Plot of $\widetilde{\psi}_\lambda(x)$ for $n \in (-5.7,-0.7)$ in unit increments.
• Figure 3: Thermal effective potentials of a two node quiver ($\theta=-1$ and $\mu=1$). As the temperature is increased the system explores various thermal configurations of stable and metastable minima. From top left to bottom right the system is of type \ref{['singstab']}$\to$\ref{['twnondeg']}$\to$\ref{['twodeg']}$\to$\ref{['twnondeg']}$\to$\ref{['q0globmin']}$\to$\ref{['hottest']}.
• Figure 4: Thermal effective potentials of a two node quiver (for $\theta=-1$ and $\mu=1$). Left: An example of phase type \ref{['q0nonglobmin']}. Right: A case where the potential of the supersymmetric minimum decreases as the temperature is increased. A similar observation was made for supersymmetric bound states in Anninos:2011vn.
• Figure 5: Thermal effective potentials of a two node quiver ($\theta=-1$ and $\mu=1$). As $\widetilde{\kappa}$ is increased we note that the first minimum disappears.