Tensor Hierarchies of 5- and 6-Dimensional Field Theories

Details Tensor Hierarchies of 5- and 6-Dimensional Field Theories Tensor Hierarchies of 5- and 6-Dimensional Field Theories

2009-06-22

arxiv.org/abs/0906.4043v1

JHEP 0909:039,2009

Physics

High Energy Physics

High Energy Physics - Theory

51 pages, 2 tables

Scientific paper

10.1088/1126-6708/2009/09/039

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.

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