Tensor Hierarchies of 5- and 6-Dimensional Field Theories

Abstract

We construct the tensor hierarchies of generic, bosonic, 5- and 6-dimensional field theories. The construction of the tensor hierarchy starts with the introduction of two tensors: the embedding tensor which tells us which vector is used for gauging and another tensor Z which tells us which vector is eaten by a 2-form. In dimensions five or more these two (deformation) tensors are in principle unrelated. Besides the embedding tensor and Z there can be further deformation tensors describing other couplings unrelated to (but compatible with) gauge symmetry. For each deformation tensor there appears a (d-1)-form potential and for each constraint satisfied by the deformation tensors there appears a d-form potential in the tensor hierarchy. For each symmetry of the undeformed theory there is an associated (d-2)-form appearing in the tensor hierarchy. Our methods easily generalize to arbitrary dimensions and we present a general construction for the d-, (d-1)- and (d-2)-form potentials for a tensor hierarchy in d dimensions.

51 pages, 2 tables

References in corpus (7)

• Lectures on Gauged Supergravity and Flux Compactifications
• E(11) and the Embedding Tensor
• Gauge Theories, Duality Relations and the Tensor Hierarchy
• Gauged Supergravities in Various Spacetime Dimensions
• The end of the p-form hierarchy
• The supersymmetric tensor hierarchy of N=1,d=4 supergravity
• Supergravity and M-Theory