2025/09/22 by Arash Arabi Ardehali, Ardehali, Arash Arabi, Mathieu Boisvert +3
Earth and Planetary Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Geophysics and Gravity Measurements #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Quantum Algebra (math.QA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2509.18285
openalex publication_date 2025/09/22 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
We study the superconformal index Z(q) of 3d N=2 gauge theories in Cardy-like limits β= log \tfrac1q → 0+, extending techniques recently developed in the 4d N=1 context. For theories with vectorlike matter content we find on the first sheet (q → 1) that Z(q) ∼ β-#, where the exponent # is determined by a multiscale decomposition of the BPS moduli space appearing in the localization formula for the index. On the second sheet (q → e2πi) we find Z(q) ∼ e#/ β, and that the long-standing puzzle of apparent gauge-enhancing saddles is resolved (in the absence of Chern--Simons couplings) via a novel Lorentzian factorization formula that establishes complete screening. A key insight is the use of Poisson resummation, which streamlines the asymptotic analysis, sharpens the link to Kaluza--Klein effective field theory, and provides a dual description of parts of the BPS moduli space in terms of punctured surfaces. The Lorentzian factorization formula also emerges from Poisson resummation, though applied after a contour crossing in moduli space. This, in turn, hints at a correspondence between 3d monopoles and vortices via 2d duality.