2023/06/02 by Fabrizio Del Monte, Del Monte, Fabrizio · 2 citations
Physics and Astronomy · #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2306.01626
openalex publication_date 2023/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper extends the correspondence between discrete Cluster Integrable Systems and BPS spectra of five-dimensional N=1 QFTs on ℝ4× S1 by proving that algebraic solutions of the integrable systems are exact solutions for the system of TBA equations arising from the BPS spectral problem. This statement is exemplified in the case of M-theory compactifications on local del Pezzo Calabi-Yau threefolds, corresponding to q-Painlevé equations and SU(2) gauge theories with matter. A degeneration scheme is introduced, allowing to obtain closed-form expression for the BPS spectrum also in systems without algebraic solutions. By studying the example of local del Pezzo 3, it is shown that when the region in moduli space associated to an algebraic solution is a ``wall of marginal stability'', the BPS spectrum contains states of arbitrarily high spin, and corresponds to a 5d uplift of a four-dimensional nonlagrangian theory.