Surface Defects and Resolvents

Abstract

We study a large class of BPS surface defects in 4d N=2 gauge theories. They are defined by coupling a 2d N=(2,2) gauged linear sigma model to the 4d bulk degrees of freedom. Our main result is an efficient computation of the effective twisted superpotential for all these models in terms of a basic object closely related to the resolvent of the 4d gauge theory, which encodes the curve describing the 4d low energy dynamics. We reproduce and extend the results of brane constructions and compute the effective twisted superpotential for general monodromy surface defects. We encounter novel, puzzling field theory phenomena in the low energy dynamics of the simplest surface defects and we propose some local models to explain them. We also study in some detail the behavior of surface defects near monopole points of the bulk theory's Coulomb branch. Finally, we explore the effect on the defect of breaking the bulk supersymmetry from N=2 to N=1 and show that certain quantities are independent of this breaking.

59 pages, 8 figures, references added

References in corpus (9)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• A Perturbative Window into Non-Perturbative Physics
• Instanton counting with a surface operator and the chain-saw quiver
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• Bubbling Surface Operators And S-Duality
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
• The BPS Spectrum Generator In 2d-4d Systems
• Surface operators in four-dimensional topological gauge theory and Langlands duality

Cited by in corpus (66)

• Comments on twisted indices in 3d supersymmetric gauge theories
• Boundary Conformal Field Theory and a Boundary Central Charge
• Defects and Quantum Seiberg-Witten Geometry
• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• (0,2) Trialities
• Dual Boundary Conditions in 3d SCFT's
• N=2 supersymmetric dynamics for pedestrians
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• tt* Geometry in 3 and 4 Dimensions
• Superconformal surfaces in four dimensions
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Liberating Confinement from Lagrangians: 1-form Symmetries and Lines in 4d N=1 from 6d N=(2,0)
• The superconformal index and an elliptic algebra of surface defects
• Mirror symmetry and line operators
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• A slow review of the AGT correspondence
• Intersecting Surface Defects and Two-Dimensional CFT
• Surface defects and instanton-vortex interaction
• Surface Defect Indices and 2d-4d BPS States
• Exploring 5d BPS Spectra with Exponential Networks
• N=1 Geometries via M-theory
• ADE Spectral Networks
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• Generalized Hitchin system, Spectral curve and N=1 dynamics
• The Quantum DELL System
• Surface operators, chiral rings, and localization in N=2 gauge theories
• Trisecting non-Lagrangian theories
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions
• A Small Deformation of a Simple Theory
• Bands and gaps in Nekrasov partition function
• Defect multiplets of N=1 supersymmetry in 4d
• Modular and duality properties of surface operators in N=2* gauge theories
• A-twisted correlators and Hori dualities
• Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories
• Boundaries and supercurrent multiplets in 3D Landau-Ginzburg models
• Surface defects on E-string from 5-brane webs
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• The energy-momentum multiplet of supersymmetric defect field theories
• ADE Spectral Networks and Decoupling Limits of Surface Defects
• Surface operators in 5d gauge theories and duality relations
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• Surface operators, dual quivers and contours
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• An infrared bootstrap of the Schur index with surface defects
• Geometry and Dynamics of a Coupled 4D-2D Quantum Field Theory
• Parallel surface defects, Hecke operators, and quantum Hitchin system
• Givental J-functions, Quantum integrable systems, AGT relation with surface operator
• Bispectral duality and separation of variables from surface defect transition
• Surface operators in N=2 SQCD and Seiberg Duality
• Surface Defects from Fractional Branes -- II
• Quantum Deformation of the Effective Theory on Non-Abelian string and 2D-4D correspondence
• Surface Defects from Fractional Branes -- I
• Surface defects and instanton partition functions
• On instability of ground states in 2D CP(N-1) and O(N) models at large N
• Dynamics of non-Abelian strings in the theory interpolating from $\mathcal{N}=2$ to $\mathcal{N}=1$ supersymmetric QCD
• Twisted-Mass Potential on the Non-Abelian String World Sheet Induced by Bulk Masses
• Surface Operators in Superspace
• Topological charges in 2d N=(2,2) theories and massive BPS states
• More Holographic M5 branes in $Ad{S}_7\times S^4$
• Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM
• Chiral rings for surface operators in 4d and 5d SQCD
• Global aspects of (0,2) moduli space: toric varieties and tangent bundles
• Painlevé Kernels and Surface Defects at Strong Coupling
• Factorized class $S$ theories and surface defects