Five-Dimensional Aspects of M-Theory Dynamics and Supersymmetry Breaking

TL;DR

The paper analyzes the two-step reduction of the M-theory effective Lagrangian from $11$D to $5$D on a Calabi--Yau and then to $4$D on $S_1/\\Z_2$, showing that the five-dimensional bulk contains a rich non-linear $\\sigma$-model for moduli coupled to gravity. Boundary sources such as gaugino condensates can trigger SUSY breaking in the hidden sector and transmit it to the visible wall through the bulk, primarily via gravity and hypermultiplets, with the transmission strength modulated by the Calabi–Yau volume and the separation of the walls. A prototype hypermultiplet sector with one universal and one non-universal hypermultiplet demonstrates how bulk dynamics and $Z_2$ parity yield non-trivial field profiles and a goldstino that can be absorbed by the four-dimensional gravitino. Three SUSY-breaking scenarios are discussed (short-, intermediate-, and long-distance origins), and the analysis shows how bulk moduli dynamics encode the boundary physics, including potential moduli stabilization and higher-order gauged supergravity corrections. The work underscores the necessity of the two-step reduction and highlights bulk–boundary mediation mechanisms for SUSY breaking relevant to realistic M-theory constructions.

Abstract

We discuss the reduction of the eleven-dimensional M-theory effective Lagrangian, considering first compactification from eleven to five dimensions on a Calabi-Yau manifold, followed by reduction to four dimensions on an S_1/Z_2 line segment at a larger distance scale. The Calabi-Yau geometry leads to a structure of the five-dimensional Lagrangian that has more freedom than the eleven-dimensional theory. In five dimensions one obtains a non-linear sigma-model coupled to gravity, which implies non-trivial dynamics for the scalar moduli fields in the bulk of the Z_2 orbifold. We discuss solutions to the five-dimensional equations of motion in the presence of sources localized on the boundaries of the Z_2 orbifold that may trigger supersymmetry breaking, e.g., gaugino condensates. The transmission of supersymmetry breaking from the hidden wall to the visible wall is demonstrated in specific models. The role of the messenger of supersymmetry breaking may be played by the gravity supermultiplet and/or by scalar hypermultiplets. The latter include the universal hypermultiplet associated with the Calabi-Yau volume, and also the hypermultiplets associated with deformations of its complex structure, which mix in general.