Vector Multiplets and the Phases of N = 2 Theories in 2D Through the Looking Glass

TL;DR

This paper explores the phases of 2D N=2 theories using vector multiplets and mirror symmetry, extending Landau-Ginzburg models to include twisted matter and vector multiplets, with conjectures on knot invariants.

Contribution

It introduces a new 2D, N=2 twisted vector multiplet and extends Landau-Ginzburg mirror models to include twisted chiral matter, revealing integrability constraints and potential links to knot invariants.

Findings

Identification of integrability obstructions in combined matter models

Extension of Landau-Ginzburg mirror symmetry to twisted vector multiplets

Conjecture linking knot invariants to the structure of these theories

Abstract

We extend Witten's discussion of actions related to the Landau-Ginzburg description of Calabi-Yau hypersurfaces in weighted projective spaces to cover the mirror class of models that include twisted chiral matter multiplets and a newly discovered 2D, N = 2 twisted vector multiplet. Certain integrability obstructions are observed that constrain the most general constructions containing both matter and twisted matter simultaneously. It is conjectured that knot invariants will ultimately play a role in describing the most general such model.