Whittaker vectors at finite energy scale, topological recursion and Hurwitz numbers

Abstract

We upgrade the results of Borot--Bouchard--Chidambaram--Creutzig to show that the Gaiotto vector in $4d$ $\mathcal{N}=2$ pure supersymmetric gauge theory admits an analytic continuation with respect to the energy scale (which can therefore be taken to be finite, instead of infinitesimal), and is computed by topological recursion on the (ramified) half Seiberg--Witten spectral curve. This has a number of interesting consequences for the Gaiotto vector: relations to intersection theory on ${\overline{\mathcal{M}}}_{g,n}$ in at least two different ways, Hurwitz numbers, quantum curves, and (almost complete) description of the correlators as analytic functions of $\hslash$ (instead of formal series). The same method is used to establish analogous results for the more general Whittaker vector constructed in the recent work of Chidambaram--Doł{ę}ga--Osuga.

arXiv comment58 pages, 1 figure; v3: minor changes, accepted for publication in J. Éc. polytech. Math

References in corpus (33)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• All genus correlation functions for the hermitian 1-matrix model
• Two Dimensional QCD is a String Theory
• Twists and Wilson Loops in the String Theory of Two Dimensional QCD
• Towards an enumerative geometry of the moduli space of twisted curves and r-th roots
• Identification of the Givental formula with the spectral curve topological recursion procedure
• N=2 supersymmetric dynamics for pedestrians
• Holomorphicity and Modularity in Seiberg-Witten Theories with Matter
• Quantum Curves and D-Modules
• A new cohomology class on the moduli space of curves
• Cut-and-join description of generalized Brezin-Gross-Witten model
• Reconstructing WKB from topological recursion
• Geometry of Spectral Curves and All Order Dispersive Integrable System
• Blobbed topological recursion: properties and applications
• Higher Genus Correlators from the Hermitian One-Matrix Model
• The ABCD of topological recursion
• Generating functions for weighted Hurwitz numbers
• Weighted Hurwitz numbers and topological recursion
• Emergent Geometry and Mirror Symmetry of A Point
• Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
• Loop equations and a proof of Zvonkine's $qr$-ELSV formula
• Topological recursion for Masur-Veech volumes
• Higher Airy structures and topological recursion for singular spectral curves
• Non-orientable branched coverings, $b$-Hurwitz numbers, and positivity for multiparametric Jack expansions
• Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
• Large N limit of 2D Yang-Mills Theory and Instanton Counting
• Whittaker vectors for $\mathcal{W}$-algebras from topological recursion
• Relations on ${\overline{\mathcal{M}}}_{g,n}$ and the negative $r$-spin Witten conjecture
• KP integrability through the $x-y$ swap relation
• Symplectic (Non-)Invariance of the Free Energy in Topological Recursion
• Taking limits in topological recursion
• On the 2D Yang-Mills/Hurwitz Correspondence
• Super volumes and KdV tau functions

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