Journal of High Energy Physics

, 2013:64

The gauge structure of generalised diffeomorphisms


  • David S. Berman
    • Centre for Research in String Theory, School of Physics, Queen Mary CollegeUniversity of London
    • Department of Fundamental PhysicsChalmers University of Technology
  • Axel Kleinschmidt
    • Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut)
    • International Solvay Institutes
  • Daniel C. Thompson
    • International Solvay Institutes
    • Theoretische Natuurkunde, Vrije Universiteit Brussel, International Solvay Institutes

DOI: 10.1007/JHEP01(2013)064

Cite this article as:
Berman, D.S., Cederwall, M., Kleinschmidt, A. et al. J. High Energ. Phys. (2013) 2013: 64. doi:10.1007/JHEP01(2013)064


We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show that the gauge algebra is infinitely reducible, i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised diffeomorphisms gives such a reducibility transformation. We give a concrete description of the ghost structure, and demonstrate that the infinite sums give the correct (regularised) number of degrees of freedom. The ghost towers belong to the sequences of representations previously observed appearing in tensor hierarchies and Borcherds algebras. All calculations rely on the section condition, which we reformulate as a linear condition on the cotangent directions. The analysis holds for n < 8. At n = 8, where the dual gravity field becomes relevant, the natural guess for the gauge parameter and its reducibility still yields the correct counting of gauge parameters.


Space-Time SymmetriesM-Theory
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© SISSA, Trieste, Italy 2013