Gauged Supergravity and Singular Calabi-Yau Manifolds

TL;DR

This paper constructs the first explicit supergravity Lagrangian for M-theory compactified on a singular Calabi-Yau threefold, demonstrating how singularities lead to gauge symmetry enhancements and their resolution corresponds to a Higgs mechanism.

Contribution

It provides a complete, explicit supergravity Lagrangian including extra charged states from singularities, fixed by Calabi-Yau geometry and the Coulomb branch, illustrating the Higgs effect in this context.

Findings

Explicit supergravity Lagrangian with charged states constructed

Singularity resolution corresponds to a supersymmetric Higgs effect

The structure is rigid and applicable to other singularities

Abstract

Compactifications of M-theory on singular manifolds contain additional charged massless states descending from M-branes wrapped on vanishing cycles. We construct the first explicit example of a complete supergravity Lagrangian that includes such extra states. This is done for a compactification on a Calabi-Yau threefold that develops a genus zero curve of A_1 singularities at the boundary of the K\"ahler cone with a resulting SU(2) gauge symmetry enhancement. The corresponding SU(2) gauged supergravity Lagrangian includes two charged and two neutral vector multiplets, and turns out to be uniquely fixed by the Calabi-Yau geometry and by the effective ungauged Lagrangian describing the Coulomb branch. One can see explicitly how resolving the singularity corresponds to a supersymmetric Higgs effect in the gauged supergravity description. The elementary transformation relating the two families of smooth Calabi-Yau resolutions of the singularity acts as the SU(2) Weyl twist. The resulting structure appears to be very rigid and is likely to apply to other types of singularities and manifolds as well.