Abstract
The action of the free theory in six spacetime dimensions is explicitly constructed. The variables of the variational principle are prepotentials adapted to the self-duality conditions on the fields. The (3, 1) supersymmetry variations are given and the invariance of the action is verified. The action is first-order in time derivatives. It is also Poincaré invariant but not manifestly so, just like the Hamiltonian action of more familiar relativistic field theories.
Highlights
The maximal supersymmetry algebra is unique in all spacetime dimensions 4 ≤ D ≤ 11, except in dimensions 6 and 10, where one can independently assign different chiralities to the supercharges [1, 2]
This is the real tensor field of mixed Young symmetry (2, 1) type with self-dual field strength described in the previous section
We have constructed the action for the free N = (3, 1) theory of “exotic supergravity” in six spacetime dimensions
Summary
The maximal supersymmetry algebra is unique in all spacetime dimensions 4 ≤ D ≤ 11, except in dimensions 6 and 10, where one can independently assign different chiralities to the supercharges [1, 2]. While the theory realizing the (2, 2) supersymmetry algebra is well known and just the toroidal dimensional reduction of maximal supergravity in 11 dimensions, the theories realizing the other two superalgebras (if they exist) are more mysterious This is because they would involve, in place of the standard spin-2 field describing gravity, tensor fields with mixed Young symmetries subject to chirality conditions. Once the variational principle for the exotic chiral (2, 1) Young symmetry field is understood, the construction of the complete action of the free N = (3, 1) theory is straightforward.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
