SU(3) × SU(3) compactification and mirror duals of magnetic fluxes

Abstract

This paper analyses type II string theories in backgrounds which admit an SU (3)×SU (3) structure. Such backgrounds are designed to linearly realize eight out of the original 32 supercharges and as a consequence the low-energy effective action can be written in terms of couplings which are closely related to the couplings of four-dimensional N = 2 theories. This generalizes the previously studied case of SU (3) backgrounds in that the left-and right-moving sector each have a different globally defined spinor. Given a truncation to a finite number of modes, these backgrounds lead to a conventional fourdimensional low-energy effective theory. The results are manifestly mirror symmetric and give terms corresponding to the mirror dual couplings of Calabi-Yau compactifications with magnetic fluxes. It is argued, however, that generically such backgrounds are nongeometric and hence the supergravity analysis is not strictly valid. Remarkably, the naive generalization of the geometrical expressions nonetheless appears to give the correct lowenergy effective theory.

Enhanced supersymmetry from vanishing Euler number

“…Subsequently, we will derive the vacuum contribution to the supersymmetry variations in terms of the internal geometry. Similar discussions can be found in [10,11,30].…”

“…[1][2][3][4][5][6]) are natural candidates for internal spaces on which to reduce the supergravity action to four dimensions in a supersymmetric fashion. 1 It has been argued in [9][10][11] that such reductions can yield supersymmetric effective theories which do not necessarily possess supersymmetric vacua. 2 We want to illustrate in this work how such off-shell supersymmetries can help in understanding quantum corrections.…”

“…The supersymmetry variations of the ten-dimensional gravitini and dilatini in the Einstein frame read [10,11,38] where the F 2n are the type IIA field strengths in the democratic formulation and the matrix Γ 11 is the chirality operator. In the following, we only consider the scalar contribution that determine the matrix A 1 .…”

“…In the following, we only write the component of positive chirality and drop the + index. The four-dimensional gravitini Ψ a µ read [10,11] …”

New examples of flux vacua

“…Performing three T-dualities is a mirror transform in the absence of flux. Some local aspects of the mirror transform with fluxes have been discussed in [56,57].…”