Observables in the equivariant A-model

TL;DR

This paper explores observables in an equivariant A-model using the AKSZ framework, introducing new classes of observables that improve gauge fixing behavior and connect to topological Yang-Mills theory.

Contribution

It introduces A-model observables that are homotopically equivalent to AKSZ observables and better suited for gauge fixing, linking to reduced spaces and supersymmetric theories.

Findings

Proposes A-model observables better behaved in gauge fixing.

Connects A-model observables to the Marsden-Weinstein reduced space.

Recovers topological Yang-Mills action with A-model observables.

Abstract

We discuss observables of an equivariant extension of the A-model in the framework of the AKSZ construction. We introduce the A-model observables, a class of observables that are homotopically equivalent to the canonical AKSZ observables but are better behaved in the gauge fixing. We discuss them for two different choices of gauge fixing: the first one is conjectured to compute the correlators of the A-model with target the Marsden-Weinstein reduced space; in the second one we recover the topological Yang-Mills action coupled with A-model so that the A-model observables are closed under supersymmetry.