The many symmetries of Calabi-Yau compactifications

Abstract

We review the major mathematical concepts involved in the dimensional reduction of D=11 N=1 supergravity theory over a Calabi-Yau manifold with non-trivial complex structure moduli resulting in ungauged D=5 N=2 supergravity theory with hypermultiplets. This last has a particularly rich structure with many underlying geometries. We reproduce the entire calculation and particularly emphasize its symplectic symmetry and how that arises from the topology of the underlying subspace. The review is intended to fill in a specific gap in the literature with the hope that it would be useful to both the beginner and the expert alike.

47 pages

References in corpus (6)

• The Anthropic Landscape of String Theory
• Five dimensional 2-branes from special Lagrangian wrapped M5-branes
• Wrapped M5-branes leading to five dimensional 2-branes
• Symplectic covariance of the N=2 hypermultiplets
• Calibrated brane solutions of M-theory
• "So what will you do if string theory is wrong?"

Cited by in corpus (6)

• Split-complex representation of the universal hypermultiplet
• The five dimensional universal hypermultiplet and the cosmological constant problem
• Zero-branes and the symplectic hypermultiplets
• Interpreting the Cosmic History of the Universe Through Five-Dimensional Supergravity
• BPS brane cosmology in N=2 supergravity
• The Hierarchy Problem and $\mathcal{N}=2$ $\mathcal{D}=5$ Supergravity