Miura operators, degenerate fields and the M2-M5 intersection

TL;DR

This paper explores the mathematical structures underlying the Omega deformation of M2-M5 brane intersections, revealing their connections to W-algebras, degenerate modules, and algebraic geometry.

Contribution

It provides a novel algebraic interpretation of the Pandharipande-Thomas counting in complex three-space related to M-brane intersections.

Findings

Connections between supersymmetric brane intersections and W-algebra structures

Algebraic interpretation of Pandharipande-Thomas counting in ^3

Insights into degenerate modules and Miura transform in this context

Abstract

We determine the mathematical structures which govern the $\Omega$ deformation of supersymmetric intersections of M2 and M5 branes. We find that the supersymmetric intersections govern many aspects of the theory of W-algebras, including degenerate modules, the Miura transform and Coulomb gas constructions. We give an algebraic interpretation of the Pandharipande-Thomas box counting in $\mathbb{C}^3$.