Monopole contributions to refined Vafa–Witteninvariants
Ties Laarakker
Abstract
We study the monopole contribution to the refined Vafa–Witten invariant recently defined by Maulik and Thomas (work in progress). We apply the results of Gholampour and Thomas (to appear in Compos. Math.) to prove a universality result for the generating series of contributions of Higgs pairs with [math] –dimensional weight spaces. For prime rank, these account for the entire monopole contribution by a theorem of Thomas. We use toric computations to determine part of the generating series and find agreement with the conjectures of Göttsche and Kool (Pure Appl. Math. Q. 14 (2018) 467–513) for ranks [math] and [math] .
Topics & Concepts
Magnetic monopoleMathematicsUniversality (dynamical systems)Invariant (physics)Higgs bosonSeries (stratigraphy)Pure mathematicsComputationRank (graph theory)Mathematical physicsAlgebra over a fieldTheoretical physicsCombinatoricsPhysicsParticle physicsQuantum mechanicsAlgorithmBiologyPaleontologyAlgebraic Geometry and Number TheoryAdvanced Algebra and GeometryFinite Group Theory Research