Five-Brane Effective Field Theory on Calabi-Yau Threefolds

TL;DR

This paper derives a four-dimensional effective supergravity Lagrangian from compactifying a dual form of 10D supergravity on Calabi-Yau threefolds, linking it to five-brane theories and string dualities.

Contribution

It constructs an off-shell N=1 supergravity effective Lagrangian in four dimensions using a dual gravitational sector, providing a new perspective on five-brane and string dualities.

Findings

Effective 4D Lagrangian derived from 10D supergravity

Connection established between supergravity and five-brane theories

Calabi-Yau compactification consistent with dual supergravity models

Abstract

We consider the compactification of the dual form of $N=1$ $D=10$ supergravity on a six-dimensional Calabi-Yau manifold. An $N=1$ off-shell supergravity effective Lagrangian in four dimensions can be constructed in a dual version of the gravitational sector (new-minimal supergravity form). Superspace duality has a simple interpretation in terms of Poincar\'{e} duality of two-form cohomology. The resulting $4D$ Lagrangian may describe the low-energy point-field limit of a five-brane theory, dual to string theory, provided Calabi-Yau spaces are consistent vacua of such dual theory.