Surface defects and instanton-vortex interaction

Abstract

We propose a simple formula for the 4d-2d partition function of half-BPS surface defects in $d=4,\mathcal{N}=2$ gauge theories: $Z^{\text{4d-2d}}=⟨Z^{\text{2d}}{⟩}_{\text{4d}}$. Our results are applicable for any surface defect obtained by gauging a 2d flavour symmetry using a 4d gauge group. For defects obtained via the Higgsing procedure, our formula reproduces the recent calculation by Pan and Peelaers. For Gukov-Witten defects our results reproduce the orbifold calculation by Kanno and Tachikawa. We emphasize the role of "negative vortices" which are realized as negative D0 branes.

arXiv commentv1: 40 pages, 8 figures, v2: clarifications and references added

References in corpus (21)

• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• The Refined Topological Vertex
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Exact Results in D=2 Supersymmetric Gauge Theories
• Vortex Counting and Lagrangian 3-manifolds
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Gluino Condensate and Magnetic Monopoles in Supersymmetric Gluodynamics
• D-branes, Monopoles and Nahm Equations
• Monopoles in the Higgs Phase
• Instantons in the Higgs Phase
• Defects and Quantum Seiberg-Witten Geometry
• Small Instantons, Little Strings and Free Fermions
• Knot homology groups from instantons
• Surface Defects and Resolvents
• Negative Branes, Supergroups and the Signature of Spacetime
• A note on instanton counting for N=2 gauge theories with classical gauge groups
• M2-brane surface operators and gauge theory dualities in Toda
• Intersecting Surface Defects and Two-Dimensional CFT
• The Condensate from Torus Knots
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• Quantum Deformation of the Effective Theory on Non-Abelian string and 2D-4D correspondence

Cited by in corpus (27)

• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Superconformal surfaces in four dimensions
• Surface Defect, Anomalies and $b$-Extremization
• Central Charges of 2d Superconformal Defects
• Mirror symmetry and line operators
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• A slow review of the AGT correspondence
• Surface operators, chiral rings, and localization in N=2 gauge theories
• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• Surface defects in gauge theory and KZ equation
• Bands and gaps in Nekrasov partition function
• 3d Expansions of 5d Instanton Partition Functions
• Intersecting Defects and Supergroup Gauge Theory
• Supersymmetric vortex defects in two dimensions
• Surface operators in 5d gauge theories and duality relations
• Surface operators, dual quivers and contours
• On Dimensional Transmutation in 1+1D Quantum Hydrodynamics
• An infrared bootstrap of the Schur index with surface defects
• Surface operators in N=2 SQCD and Seiberg Duality
• Surface Defects from Fractional Branes -- II
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Surface Defects from Fractional Branes -- I
• Intersecting Surface defects and 3d Superconformal indices
• More Holographic M5 branes in $Ad{S}_7\times S^4$
• Chiral rings for surface operators in 4d and 5d SQCD
• Modular properties of surface operators in N=2 SQCD
• Painlevé Kernels and Surface Defects at Strong Coupling