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

TL;DR

This paper explores folding techniques applied to Calabi-Yau diagrams in M-theory, revealing how black brane configurations on a tetra-quadric Calabi-Yau can be simplified to lower-dimensional models.

Contribution

It introduces a novel folding procedure for Calabi-Yau diagrams, connecting complex five-dimensional black brane scenarios to simpler, well-understood compactifications.

Findings

Folding reduces complex Calabi-Yau diagrams to known models.

New features emerge from combining graph theory and automorphism techniques.

Black branes on tetra-quadric Calabi-Yau relate to lower-dimensional cases.

Abstract

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{CP}^{1}\times\mathbb{CP}^{1}\times\mathbb{CP}^{1}\times\mathbb{CP}^{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 K\"{a}hler moduli spaces.