IIB Supergravity and the E6(6) covariant vector-tensor hierarchy

TL;DR

This paper reformulates IIB supergravity to make its symmetries and embedding into five-dimensional supergravity transparent, revealing the structure of vector-tensor hierarchies and their relation to dual gravitons.

Contribution

It introduces a manifest USp(8) invariant formulation of IIB supergravity that clarifies the embedding of five-dimensional maximal supergravities and reproduces the E6(6) symmetric tensor within this framework.

Findings

Reproduces the E6(6) symmetric tensor in the reformulated theory.

Derives generalized vielbeine and covariant fermion expressions.

Discusses implications for consistent truncation on the five-sphere.

Abstract

IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and 22 of the 27 two-form fields that are required by the vector-tensor hierarchy of the five-dimensional theory. The missing 5 two-form fields must transform in the same representation as a descendant of the ten-dimensional `dual graviton'. The invariant E6(6) symmetric tensor that appears in the vector-tensor hierarchy is reproduced. Generalized vielbeine are derived from the supersymmetry transformations of the vector fields, as well as consistent expressions for the USp(8) covariant fermion fields. Implications are discussed for the consistency of the truncation of IIB supergravity compactified on the five-sphere to maximal gauged supergravity in five space-time dimensions with an SO(6) gauge group.