Work

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

Year: 2025

Type: article

Abstract: We upgrade the results of Borot–Bouchard–Chidambaram–Creutzig [BBCC24] to show that the Gaiotto vector in 4 d 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 ℳ ¯ g , n in at least two different ways, Hurwitz numbers, quantum curves, and (almost complete) description of the correlators as analytic functions of ℏ (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–Dołęga–Osuga [CDO24].

Source: Journal de l’École polytechnique — Mathématiques

DOI: 10.5802/jep.316

Authors: Gaëtan Borot, Nitin Kumar Chidambaram, Giacomo Umer

Institutions: Universidad Nacional de Educación a Distancia, Humboldt-Universität zu Berlin

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: H2020 European Research Council

Award: Non-compact Chern-Simons Theory, Positive Representations, and Cluster Varieties