N=8 gaugings revisited: an exhaustive classification

TL;DR

This paper provides a comprehensive classification of all possible gaugings in N=8 supergravity, showing that the known models are exhaustive and identifying the unique abelian gauging.

Contribution

It offers an algebraic framework characterizing all admissible gaugings in N=8 supergravity, confirming the completeness of previously known models.

Findings

Complete set of solutions characterized by 36 parameters.

Established the correspondence with real forms of SO(8) Lie algebra.

Proved the known models are exhaustive and identified a unique abelian gauging.

Abstract

In this paper we reconsider, for N=8 supergravity, the problem of gauging the most general electric subgroup. We show that admissible theories are fully characterized by a single algebraic equation to be satisfied by the embedding of the gauge group G within the electric subalgebra SL(8,\IR) of E_{7(7)}. The complete set of solutions to this equation contains 36 parameters. Modding by the action of SL(8,\IR) conjugations that yield equivalent theories all continuous parameters are eliminated except for an overall coupling constant and we obtain a discrete set of orbits. This set is in one--to--one correspondence with 36 Lie subalgebras of SL(8,\IR), corresponding to all possible real forms of the SO(8) Lie algebra plus a set of contractions thereof. By means of our analysis we establish the theorem that the N=8 gaugings constructed by Hull in the middle eighties constitute the exhaustive set of models. As a corollary we show that there exists a unique 7--dimensional abelian gauging. The corresponding abelian algebra is not contained in the maximal abelian ideal of the solvable Lie algebra generating the scalar manifold E_{7(7)}/SU(8).