Torsion-Free Generalized Connections and Heterotic Supergravity

Degenerate torsion-free G3-connections revisited

between any two coordinates ( i) and ( i). Hence any choice of Γ k ij in one coordinate chart suffices to define the connection in another. Let T k ij := Γkij − Γkji be the torsion tensor of the connection. The case when torsion is zero (torsion-free) is of particular interest in geometry. In Hermann Weyl’s terms [11], the very existence of inertia systems in the Universe warrants that its line...

Heterotic Strings with Torsion

In this paper we describe the heterotic dual of the type IIB theory compactified to four dimensions on a toroidal orientifold in the presence of fluxes. The type IIB background is most easily described in terms of an M-theory compactification on a four-fold. The heterotic dual is obtained by performing a series of U -dualities. We argue that these dualities preserve supersymmetry and that the s...

Torsion-free Sheaves and Moduli of Generalized Spin Curves

This article treats the compactification of the space of higher spin curves, i.e. pairs (X,L) with L an r root of the canonical bundle of X. More precisely, for positive integers r and g, with g > 2, r dividing 2g − 2, and for a flat family of smooth curves f : X → T, an r-spin structure on X is a line bundle L such that L ∼= ωX /T . And an r-spin curve over T is a flat family of smooth curves ...

Properties of Generalized Berwald Connections

Discrete Torsion in Perturbative Heterotic String Theory

In this paper we analyze discrete torsion in perturbative heterotic string theory. In previous work we have given a purely mathematical explanation of discrete torsion as the choice of orbifold group action on a B field, in the case that dH = 0; in this paper we perform the analogous calculations in heterotic strings where dH = 0.