On the mathematics and physics of Mixed Spin P-Fields

TL;DR

This paper explores the mathematical and physical aspects of Mixed Spin P-Fields, connecting algebraic geometry with Landau Ginzburg models and introducing a new framework for path integral measures.

Contribution

It introduces the theory of Mixed Spin P-Fields and develops algebro-geometric techniques for constructing path integral measures in this context.

Findings

Development of affine and general Landau Ginzburg models in physics.

Construction of virtual fundamental classes using cosection localization.

Formulation of Mixed Spin P-Fields theory.

Abstract

We outline various developments of affine and general Landau Ginzburg models in physics. We then describe the A-twisting and coupling to gravity in terms of Algebraic Geometry. We describe constructions of various path integral measures (virtual fundamental class) using the algebro-geometric technique of cosection localization, culminating in the theory of ``Mixed Spin P (MSP) fields" developed by the authors.