Quantum TBA for refined BPS indices

2025/07/22 by Sergei Alexandrov, Alexandrov, Sergei, Khalil Bendriss +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2507.16908

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

Refined BPS indices give rise to a quantum Riemann-Hilbert problem that is inherently related to a non-commutative deformation of moduli spaces arising in gauge and string theory compactifications. We reformulate this problem in terms of a non-commutative deformation of a TBA-like equation and obtain its formal solution as an expansion in refined indices. As an application of this construction, we derive a generating function of solutions of the TBA equation in the unrefined case.

Citations

• Mock modularity at work, or black holes in a forest
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
• Enumerative Geometry of Quantum Periods
• Refined Gromov-Witten invariants
• Hypermultiplet metric and NS5-instantons
• The threefold way to quantum periods: WKB, TBA equations and q-Painlevé
• Conformal TBA for resolved conifolds
• Heavenly metrics, BPS indices and twistors
• Geometry from Donaldson-Thomas invariants
• S-duality and refined BPS indices
• A quantized Riemann-Hilbert problem in Donaldson-Thomas theory
• K3 metrics from little string theory
• Black holes and higher depth mock modular forms
• Attractor flow trees, BPS indices and quivers
• Multiple D3-instantons and mock modular forms II
• Twistorial Topological Strings and a tt* Geometry for N=2 Theories in 4d
• Y systems, Q systems, and 4D N=2 supersymmetric QFT
• Stability data, irregular connections and tropical curves
• Opers and TBA
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations

Related

• S-duality and refined BPS indices
• Black holes and dualities in string theory compactifications
• Conformal TBA for resolved conifolds
• BPS Spectra and Algebraic Solutions of Discrete Integrable Systems
• Quantum geometry, stability and modularity