A heterotic sigma model with novel target geometry

TL;DR

This paper introduces a new heterotic sigma model with a complex Lie algebroid target space on a Kähler manifold, revealing novel topological twists and associated algebraic structures linked to Lie algebroid cohomology.

Contribution

It constructs a heterotic sigma model with a transitive Lie algebroid target and explores its topological twists and algebraic structures, a novel geometric framework.

Findings

Two topological half--twists leading to A and B models identified.

Each model has two inequivalent BRST structures and associated chiral algebras.

Chiral rings characterized via Lie algebroid cohomology in the classical limit.

Abstract

We construct a (1,2) heterotic sigma model whose target space geometry consists of a transitive Lie algebroid with complex structure on a Kaehler manifold. We show that, under certain geometrical and topological conditions, there are two distinguished topological half--twists of the heterotic sigma model leading to A and B type half--topological models. Each of these models is characterized by the usual topological BRST operator, stemming from the heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with the former, originating from the (1,0) supersymmetry. These BRST operators combined in a certain way provide each half--topological model with two inequivalent BRST structures and, correspondingly, two distinct perturbative chiral algebras and chiral rings. The latter are studied in detail and characterized geometrically in terms of Lie algebroid cohomology in the quasiclassical limit.