Degeneration of Groups of Type E7 and Minimal Coupling in Supergravity

TL;DR

This paper analyzes how certain duality groups in supergravity theories degenerate and how these degenerations influence minimal coupling, with implications for cosmology and black-hole solutions.

Contribution

It provides a detailed classification of E7 group degenerations and explores their impact on vector couplings in supergravity models.

Findings

Degeneration of E7 duality groups leads to perfect square invariants.

Consistent truncation to N=1 supergravity results in minimal vector coupling.

Non-minimal couplings involving vectors, scalars, and axions are common.

Abstract

We study properties of D = 4, N >1 extended supergravities (and related compactifications of superstring theory) and their consistent truncation to the phenomenologically interesting models of N = 1 supergravity. This involves a detailed classification of the "degenerations" of the duality groups of type E7, when the corresponding quartic invariant polynomial built from the symplectic irreducible representation of G4 "degenerates" into a perfect square. With regard to cosmological applications, we conclude that the consistent truncation to N = 1 from higher-dimensional or higher-N theory gives a zero measure minimal coupling of vectors. A non-minimal coupling involving vectors coupled to scalars and axions is generic. These features of supergravity, following from the electric-magnetic duality, may be useful in other applications, like stabilization of moduli, and in studies of non-perturbative black-hole solutions of supergravity/string theory.