Heterotic fluxes and supersymmetry

Abstract

We show that the formal α ′ expansion for heterotic flux vacua is only sensible when flux quantization and the appearance of string scale cycles in the geometry are carefully taken into account. We summarize a number of properties of solutions with N=1 and N=2 space-time supersymmetry.

Gaugino condensation and the cosmological constant

“…There, the leading order solutions were shown to be a Ricci flat manifold with constant φ and vanishing H. A non-trivial dilaton or H are only permitted at O(α ′ ). This has also been emphasized more recently (at least for supersymmetric solutions) in [31] and [32]. There too, it has been noted that H is α ′ suppressed, and the only supersymmetric solutions consistent with an α ′ expansion are Calabi-Yau at leading order.…”

Non-duality in three dimensions

“…In order to discuss spinors and their properties on X 7 let us first fix a basis for the Clifford algebra. 7 Clifford algebra on X 7 . We choose the Γ i , i = 1, .…”

“…The latter have been the focus of much attention, e.g. [4][5][6][7], and remain the sole compact examples of heterotic flux vacua.…”

Generalised geometry for string corrections

“…Such an approach was used to reproduce the heterotic dynamics using generalised geometry 4 We shall denote the dimension of the space-time by n (typically n = 10 or rather n = (1, 9)). When we talk about the backgrounds with isometries or dimensional reductions the number of compact dimensions will be denoted by d. 5 Heterotic flux (torsionful) backgrounds provide a natural context for applying these constructions [40,41] The role of torsionful connections (1.2) in heterotic backgrounds has been discussed in [42]. 6 As will be discussed in subsection 3.4 the connection may be restricted by extra requirements, such as T-duality covariance.…”

“…we can solve (3.33) byH 42) where A ± are the gauge connections for F ± = 1 2 (G 2 ± G 2 ). Furthermore, the two-form gauge fieldB 2 appears in the decomposition of B as…”