On Folding Calabi-Yau Diagrams in M-theory Black Brane Scenarios

In this paper, we reconsider the study of five-dimensional supersymmetric black branes in the context of the M-theory compactification on a special Calabi-Yau manifold called tetra-quadric, being realized as complete intersections of homogenous polynomials in the projective space ${\mathbb{C}\mathbb{P}}^1\times {\mathbb{C}\mathbb{P}}^1\times {\mathbb{C}\mathbb{P}}^1\times {\mathbb{C}\mathbb{P}}^1$. Combining colored graph theory and outer-automorphism group action techniques, we approach the tetra-quadric Calabi-Yau diagram leading to new features. Using a procedure referred to as folding, we show that M-theory black branes on the tetra-quadric Calabi-Yau manifold can be reduced to known compactifications with lower dimensional Kähler moduli spaces.