Roberto Zucchini
A Heterotic Sigma Model with Novel Target Geometry
Preprint series: ESI preprints

MSC:

81T20 Quantum field theory on curved space backgrounds

53C99 None of the above but in this section

PACS: 04.62.+v02.40.-k
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.


Keywords: quantum field theory in curved spacetime, geometry, differential geometry and topology