Heterotic flux backgrounds and their IIA duals

Abstract

We study four-dimensional heterotic flux vacua with N = 2 spacetime supersymmetry. A worldsheet perspective is used to clarify quantization conditions associated to the fluxes and the constraints these place on the moduli spaces of resulting compactifications. We propose that these vacua fit naturally in the context of heterotic/IIA duality as heterotic duals to compactifications on K3-fibered but not elliptically fibered Calabi-Yau three-folds. We present some examples of such potential dual pairs.

The Infinitesimal Moduli Space of Heterotic G 2 Systems

“…In the bulk of the paper we have replaced θ in with a more general connectioñ θ in the appropriate places. Ambiguities surrounding the connectionθ have been discussed extensively in the literature before [75,82,[84][85][86][87][88][89][90][91][92]. In particular, it has been argued that deforming this connection can equivalently be interpreted as a field redefinition, though care most be taken when performing such redefinitions as they in general also lead to corrections to the supersymmetry transformations and equations of motion.…”

Non-duality in three dimensions

“…It is possible, while preserving N = 1, 2, 3 three-dimensional super-Poincaré invariance, 1 to choose G with a component that threads the volumes of the two K3 factors. Such a volume-threading flux automatically obstructs a lift to M-theory on K3 × R 1,6 , so that we cannot apply a standard duality with heterotic string on T 3 × R 1,6 .…”

“…At first sight, the question itself might appear strange. The background with flux is not a solution of the equations of motion with an R 1,6 Minkowski spacetime. This is easy to see for an unwarped spacetime metric from the M-theory equations of motion, 4) since the spacetime Ricci tensor, which should vanish, is sourced by the flux.…”

“…That is the familiar condition for preserving N = 2 supersymmetry [21]. 6 That is, the Ja are three non-degenerate two-forms that satisfy the defining cubic and quartic relations…”

“…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.…”