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 $SO(1,1)\times SO(4)$. 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.
Highlights
The Lagrangian formulation of self-dual or duality-symmetric fields is essentially not unique, but is related to different possible ways of tackling the issue of space-time invariance of the duality-symmetric actions
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)
In this paper we have analysed a possibility of supersymmetrising and coupling to gravity the free theory for the 2-form chiral gauge field in six-dimensional space-time in the formulation with the manifest SO(1, 1) × SO(4) invariance [23] and generalize it to include non-linear self-interactions of a Born-Infeld type
Summary
The Lagrangian formulation of self-dual or duality-symmetric fields is essentially not unique, but is related to different possible ways of tackling the issue of (non-manifest) space-time invariance of the duality-symmetric actions (see e.g. [4, 15,16,17,18,19,20,21,22]). Various possible ways of constructing actions which produce the (self)-duality relations as (a consequence of) equations of motion by effectively splitting d-dimensional space-time into pand q-dimensional subspaces, with d = p + q, were explored for free theories in flat space in [23, 24] In these formulations only SO(1, p − 1) × SO(q) subgroup of the SO(1, d − 1) Lorentz symmetry is manifest, while the complete 6d invariance is realized in a non-manifest (modified) form. As suggested by Hamiltonian analysis, coupling to 6d gravity might be possible
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