Gaugings from E7 Extended Geometries

TL;DR

This paper explores the construction of gaugings in E7 Extended Geometries, focusing on SL(8) truncations, and demonstrates how certain gaugings like SO(8) can be generated or not within these frameworks.

Contribution

It provides a simplified method for finding gaugings in E7 Extended Geometries using SL(8) truncations and clarifies limitations in generating certain dyonic gaugings.

Findings

Derived internal generalized vielbein for the seven sphere.

Showed that SL(8) sectors cannot generate new SO(8) dyonic gaugings.

Provided a new perspective on the generation of SO(8) gaugings.

Abstract

We discuss the construction of gaugings in recent models of E7 Extended Geometries, focusing on the two inequivalent SL(8) truncations of the theory. In these sectors the conditions for the generation of gaugings in the 36, 36', 420 and 420' representations of E7 can be compactly expressed in terms of objects which are in the fundamental representation of SL(8), making the search of solutions simpler. As an application we discuss the generation of SO(8) gaugings. In particular we show how the internal generalized vielbein for the seven sphere recently found by Nicolai et al. can be derived in a completely independent setting and we also prove that neither of these sectors is able to generate the new SO(8) dyonic gaugings, at least if the so called section conditions are implemented.