The Equivariant B model

TL;DR

This paper introduces an equivariant deformation of the $B$ model on the sphere, enabling new position-dependent observables and revealing novel features in superpotential and complex structure deformations.

Contribution

It presents a new equivariant $B$ model with modified supersymmetry, expanding the scope of observables and exploring its behavior under specific deformations.

Findings

Introduction of position-dependent observables

Distinct behavior under superpotential deformations

New features in complex structure deformations

Abstract

In this work, we introduce an equivariant deformation of the $B$ model on the sphere with a $U(1)$-action. We present the deformed supersymmetry transformations and corresponding Lagrangians and study observables in the supercharge cohomology. The inclusion of equivariance allows for the introduction of novel, position-dependent observables on the sphere, which have no counterparts in the conventional $B$ model. Two specific cases we explore in detail are position-dependent superpotentials and complex structure deformations. In both instances, the theory exhibits notable differences from the standard $B$ model, revealing intriguing new features.