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HEIndividual fellowship2023–2025

Quivers · AdS(2)/CFT(1) holography via quiver quantum mechanics

Horizon Europe — Marie Skłodowska-Curie Actions

Duration
2023-04-11 → 2025-04-10
EU contribution
€150,439
Participants
4
Scheme
HORIZON-TMA-MSCA-PF-EF

Lines connect the coordinator with its partners.

Results in brief

AdS(2)/CFT(1) holography via quiver quantum mechanics

Black holes are key to understanding the deep connection between gravity and quantum mechanics. While general relativity predicts the macroscopic behavior of black holes, it does not explain their microscopic structure. Quantum theory suggests that black holes carry entropy, implying the existence of countless hidden microstates, but a precise description of these states is still missing. This is known as the Black Hole Microstructure Problem (BHMP), a long-standing and fundamental challenge in theoretical physics. The QUIVERS project tackled this problem by studying the quantum mechanics of D-brane bound states—objects arising in string theory that can be used to model black holes at the microscopic level. Specifically, it focused on a class of supersymmetric systems known as Type-B superconformal quantum mechanics, which are believed to capture the physics near the horizon of extremal black holes. The central objective of the project was to compute a refined mathematical object called the superconformal index, which counts the number of quantum ground states protected by symmetry. These indices were calculated for models with singular and non-compact geometries, using advanced localization and regularization techniques. The results were then compared with entropy predictions from supergravity theories, providing a direct test of the AdS(2)/CFT(1) holographic correspondence, a conjectured duality between gravitational systems and quantum mechanics. QUIVERS thus provided new tools to quantify black hole microstates and offered one of the first concrete examples of AdS(2)/CFT(1) duality beyond idealized or simplified setups. This contributes not only to quantum gravity research but also to mathematical physics, as the methods developed intersect with topics in geometry and index theory. In line with the EU’s goals to support frontier science and interdisciplinary collaboration, QUIVERS enhances our understanding of quantum black holes and strengthens Europe's role in fundamental theoretical research.

Data: CORDIS, © European Union

Project objective

Identifying the near-horizon black hole microstates which produce the correct black hole entropy formula is a fundamental open problem in theoretical physics, and at the same time, it is the ultimate aim of AdS/CFT holography. Quiver quantum mechanics captures the bound states of D-brane constituents of 4-dimensional extremal black holes. It is a unique description compared to all previously known examples of CFTs in the context of AdS/CFT correspondence because it allows a direct interpretation of its ground states as bound states of BPS (Bogomolny-Prasad-Sommerfield) black holes in four-dimensional supergravity.Conformal symmetry appears in the scaling limit of the effective Coulomb branch quiver mechanics. We recently developed a geometric gauged sigma model reformulation for this model as a type-B superconformal mechanics. It is a powerful interpretation because it provides a differential geometric description for the Hilbert space. Using this formulation as our groundwork, we will obtain a definitive result for the ground state degeneracies of the scaling quiver quantum mechanics by applying regularisation and Atiyah-Bott localisation techniques that were applied before for type-A superconformal mechanical models. Furthermore, this computation will provide the first-ever superconformal index computation for type-B models. Through the microscopic entropy computation, we will obtain an identification of the ground states of quiver D-brane quantum mechanics with pure AdS(2) black hole microstates, and hence the first ever evidence for the pure AdS(2)/CFT(1) holography. We will use this result to resolve long-standing problems about the AdS(2) BPS black holes in the supergravity regime. For example, we will determine the existence of a possible (topological) quantum hair for AdS(2) scaling black holes, thereby obtaining concrete evidence either for the traditional empty-space or the fuzzball picture for the horizon neighbourhood of this class of black holes.

Original text from CORDIS.

Participants

  • FYZIKALNI USTAV AV CR, VVI · PRAHA 8CoordinatorCzechia
  • NATIONAL TAIWAN UNIVERSITY · TaipeiTaiwan
  • OKINAWA INSTITUTE OF SCIENCE AND TECHNOLOGY SCHOOL CORPORATION GAKO HOJIN · OkinawaJapan
  • THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE · CAMBRIDGEUnited Kingdom

Links

Data: CORDIS, © European Union