Surface operators, chiral rings, and localization in N=2 gauge theories

Abstract

We study half-BPS surface operators in supersymmetric gauge theories in four and five dimensions following two different approaches. In the first approach we analyze the chiral ring equations for certain quiver theories in two and three dimensions, coupled respectively to four- and five-dimensional gauge theories. The chiral ring equations, which arise from extremizing a twisted chiral superpotential, are solved as power series in the infrared scales of the quiver theories. In the second approach we use equivariant localization and obtain the twisted chiral superpotential as a function of the Coulomb moduli of the four- and five-dimensional gauge theories, and find a perfect match with the results obtained from the chiral ring equations. In the five-dimensional case this match is achieved after solving a number of subtleties in the localization formulas which amounts to choosing a particular residue prescription in the integrals that yield the Nekrasov-like partition functions for ramified instantons. We also comment on the necessity of including Chern-Simons terms in order to match the superpotentials obtained from dual quiver descriptions of a given surface operator.

41 pages. v3: typos corrected in the text and in some formulae. Some sentences rephrased according to the suggestions of the referee. Matches the version published on JHEP

References in corpus (30)

• Phases of $N=2$ Theories In Two Dimensions
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• Supersymmetric vacua and Bethe ansatz
• D-particle bound states and generalized instantons
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Quantum integrability and supersymmetric vacua
• Multi-Instanton Calculus and Equivariant Cohomology
• Five Dimensional Gauge Theories and Relativistic Integrable Systems
• Branes and N=2 Theories in Two Dimensions
• Matrix Models, Geometric Engineering and Elliptic Genera
• Defects and Quantum Seiberg-Witten Geometry
• Surface Operators in N=2 4d Gauge Theories
• Affine SL(2) conformal blocks from 4d gauge theories
• On Three Dimensional Quiver Gauge Theories and Integrability
• Matone's Relation in the Presence of Gravitational Couplings
• The Effective Prepotential of N=2 Supersymmetric SU(N_c) Gauge Theories
• Instanton counting with a surface operator and the chain-saw quiver
• The equivariant A-twist and gauged linear sigma models on the two-sphere
• Surface Defects and Resolvents
• Dynamics of N=2 Supersymmetric Chern-Simons Theories
• Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories
• The N=2 gauge theory prepotential and periods from a perturbative matrix model calculation
• Mirror Symmetry in 2+1 and 1+1 Dimensions
• IR Dualities in General 3d Supersymmetric SU(N) QCD Theories
• Surface defects and instanton-vortex interaction
• A 5d/3d duality from relativistic integrable system
• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• Modular and duality properties of surface operators in N=2* gauge theories
• Chiral observables and S-duality in N = 2* U(N) gauge theories

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• Bands and gaps in Nekrasov partition function
• 3d defects in 5d: RG flows and defect F-maximization
• Surface operators in 5d gauge theories and duality relations
• Surface operators, dual quivers and contours
• Surface Defects from Fractional Branes -- I
• Surface Operators in Superspace
• 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