New supersymmetric flux vacua with intermediate SU(2) structure
David Andriot
TL;DR
The paper addresses the landscape of four-dimensional Minkowski flux vacua in type II string theory by incorporating intermediate $SU(2)$ structure on nilmanifolds and solvmanifolds. It introduces a projection basis that diagonalizes orientifold projections and reveals a link to dielectric pure spinors, enabling a tractable solution of the SUSY equations. Three new vacua are found, two of which are related by T-duality, and none arise from T-duality with warped ${T}^6$ and ${O3}$; the work also recovers known Scan solutions as limits, providing intuition for dynamical $SU(3) imes SU(3)$ structures. The results broaden the known flux vacua and offer a concrete framework for studying intermediate structures, with implications for the string landscape and potential dynamical realizations.
Abstract
We find new supersymmetric four-dimensional Minkowski flux vacua of type II string theory on nilmanifolds and solvmanifolds. We extend the results of M. Grana, R. Minasian, M. Petrini, and A. Tomasiello to the case of intermediate SU(2) structures (the two internal supersymmetry parameters are neither parallel nor orthogonal). As pointed out recently by P. Koerber and D. Tsimpis, intermediate SU(2) structures are possible when one considers "mixed" orientifold projection conditions. To find our vacua, we rewrite these projection conditions in a more tractable way by introducing new variables: the projection basis. In these variables, the SUSY conditions become also much simpler to solve, and we find three new vacua. In addition, we find that these variables correspond to the SU(2) structure appearing with the dielectric pure spinors, objects introduced and discussed by R. Minasian, M. Petrini, A. Zaffaroni, and N. Halmagyi, A. Tomasiello, in the AdS/CFT context. Besides, our solutions provide some intuition on what a dynamical SU(3) x SU(3) structure solution could look like.