A symplectic rearrangement of the four dimensional non-geometric scalar potential

Abstract

We present a symplectic rearrangement of the effective four-dimensional non-geometric scalar potential resulting from type IIB superstring compactification on Calabi Yau orientifolds. The strategy has two main steps. In the first step, we rewrite the four dimensional scalar potential utilizing some interesting flux combinations which we call new generalized flux orbits. After invoking a couple of non-trivial symplectic relations, in the second step, we further rearrange all the pieces of scalar potential into a completely `symplectic-formulation' which involves only the symplectic ingredients (such as period matrix etc.) without the need of knowing Calabi Yau metric. Moreover, the scalar potential under consideration is induced by a generic tree level K\"{a}hler potential and (non-geometric) flux superpotential for arbitrary numbers of complex structure moduli, K\"ahler moduli and odd-axions. Finally, we exemplify our symplectic formulation for the two well known toroidal examples based on type IIB superstring compactification on ${\mathbb T}^6/{({\mathbb Z}_2 \times {\mathbb Z}_2)}$-orientifold and ${\mathbb T}^6/{{\mathbb Z}_4}$-orientifold.