A Note On The Semiclassical Formulation Of BPS States In Four-Dimensional N=2 Theories

Abstract

Vector spaces of (framed) BPS states of Lagrangian four-dimensional N=2 field theories can be defined in semiclassical chambers in terms of the $L^2$-cohomology of Dirac-like operators on monopole moduli spaces. This was spelled out previously for theories with only vectormultiplets, taking into account only a subset of the possible half-supersymmetric 't Hooft-Wilson line defects. This note completes the discussion by describing the modifications needed when including matter hypermultiplets together with arbitrary 't Hooft-Wilson line defects. Two applications of this extended discussion are given.

21 pages, 1 figure. Submitted to the PTEP Special Section "Nambu, A Foreteller of Modern Physics III" (Chicago Symposium)

References in corpus (7)

• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• Holomorphic reduction of N=2 gauge theories, Wilson-'t Hooft operators, and S-duality
• Parameter counting for singular monopoles on R^3
• Brane bending and monopole moduli
• Semiclassical framed BPS states
• Monopoles and Wilson Lines
• L^2-Kernels Of Dirac-Type Operators On Monopole Moduli Spaces

Cited by in corpus (7)

• Monopole Bubbling via String Theory
• Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I
• Index-Like Theorems from Line Defect Vevs
• Wall Crossing from Dirac Zeromodes
• Quivers, Line Defects and Framed BPS Invariants
• Index-like Theorem for Massless Fermions in Spherically Symmetric Monopole Backgrounds
• Supersymmetry of the D3/D5 Defect Field Theory