The QUIVERS project was structured around the goal of computing superconformal indices for Type-B supersymmetric quantum mechanical models, which describe the dynamics of D-brane bound states relevant to black hole microphysics. These models are highly non-trivial due to their singular, non-compact target space geometries and the reduced amount of supersymmetry they preserve.
The work proceeded in three main stages:
Algebraic foundation and representation theory:
The project began with a systematic classification of irreducible representations of the relevant superconformal algebras, su(1,1∣1) and D(2,1;α), identifying the short (BPS) multiplets that contribute to the ground state spectrum. This established the algebraic structure needed to define the superconformal index.
Localization and regularization techniques:
A major achievement was the development and implementation of localization methods tailored to Type-B models, allowing for exact index computations even on singular and non-Kähler spaces. These techniques adapted known geometric tools to a new class of supersymmetric quantum systems and allowed for reliable extraction of physical degeneracies.
Explicit examples and holographic interpretation:
Two representative models—one with α=0 and one with α≠0—were canonically quantized. Their spectra were analyzed independently of localization, and the resulting indices matched those from the localization framework, validating the methodology. These results were then interpreted in the context of black hole entropy, supporting the AdS(2)/CFT(1) correspondence. The project also identified a twist structure in the metrics of quiver models, which resemble the analog property of the corresponding supergravity solutions. Overall, the project produced novel analytic tools, exact index formulas, and a consistent holographic picture for extremal black holes. These achievements were documented in four peer-reviewed articles and two forthcoming submissions, marking a significant contribution to the field of quantum gravity and supersymmetric quantum mechanics.
