Riemann-Hilbert correspondence and blown up surface defects

Abstract

The relationship of two dimensional quantum field theory and isomonodromic deformations of Fuchsian systems has a long history. Recently four-dimensional $\mathcal{N}=2$ gauge theories joined the party in a multitude of roles. In this paper we study the vacuum expectation values of intersecting half-BPS surface defects in $SU(2)$ theory with $N_f=4$ fundamental hypermultiplets. We show they form a horizontal section of a Fuchsian system on a sphere with $5$ regular singularities, calculate the monodromy, and define the associated isomonodromic tau-function. Using the blowup formula in the presence of half-BPS surface defects, initiated in the companion paper, we obtain the GIL formula, establishing an unexpected relation of the topological string/free fermion regime of supersymmetric gauge theory to classical integrability.

arXiv comment94 pages; v2. references added, published version

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Cited by in corpus (24)

• Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
• Accessory parameters in confluent Heun equations and classical irregular conformal blocks
• Surface defects in gauge theory and KZ equation
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• 5d/6d Wilson loops from blowups
• Instanton counting and O-vertex
• Scalar/Dirac perturbations of the Reissner-Nordström black hole and Painlevé transcendents
• A geometric recipe for twisted superpotentials
• Intersecting Defects and Supergroup Gauge Theory
• Quantum spectral problems and isomonodromic deformations
• Tetrahedron instantons
• ABCD of qq-characters
• M2-branes and $\mathfrak{q}$-Painlevé equations
• di-Langlands correspondence and extended observables
• Parallel surface defects, Hecke operators, and quantum Hitchin system
• Holographic Generalised Gukov-Witten Defects
• R-matrices and Miura operators in 5d Chern-Simons theory
• Bispectral duality and separation of variables from surface defect transition
• Intersecting Surface defects and 3d Superconformal indices
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations
• Painlevé Kernels and Surface Defects at Strong Coupling
• Highest-weight vectors and three-point functions in GKO coset decomposition