Abstract
We present an attempt to formulate an action for the worldvolume theory of a single M5-brane, based on the splitting of the six worldvolume directions into 2+4, which breaks manifest Lorentz invariance from SO(1, 5) to SO(1, 1) × SO(4). To this end, an action for the free six-dimensional (2,0) chiral tensor multiplet, and separately, a nonlinearly interacting chiral 2-form action are constructed. By studying the Lagrangian formulation for the chiral 2-form with 2+4 splitting, it is suggested that, if exists, the modified diffeomorphism of the theory on curved six-dimensional space-time is less trivial than its 1+5 and 3+3 counterpart, thus hindering the coupling of the chiral 2-form to the induced metric on the worldvolume of the M5-brane. We discuss difficulties of further generalisation of the theory. Finally, in terms of Hamiltonian analysis, we show that the naively gauge-fixed failed-PST-covariantised Lagrangian has the correct number of degrees of freedom, and satisfies the hyper-surface deformation algebra.
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Ko, SL., Vanichchapongjaroen, P. Towards 2+4 formulation of M5-brane. J. High Energ. Phys. 2015, 1–26 (2015). https://doi.org/10.1007/JHEP12(2015)170
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DOI: https://doi.org/10.1007/JHEP12(2015)170