Fermions in odd dimensions

1. Some reference papers A. Bashir, Ma. de Jesus Anguiano Galicia Fermions in odd space-time dimensions: back to basics Few-Body Systems 0, 1–8 (2008),hep-ph/0502089v1 C. Burden, A. N. Burkitt Lattice Fermions in Odd Dimensions Europhys. Lett., 3 (5), pp. 545-552 (1987) W. Bietenholz, J, Nishimura Ginsparg-Wilson fermions in odd dimensions JHEP07(2001)015, hep-lat/0012020v2 Y. Kikukawa, H. Neuberger Overlap in odd dimensions Nucl. Phys. B, 513-3 (1998) 735, hep-lat/9707016v1 Fermions in odd dimensions

2. In odd dimensions the Clifford algebra does not admit a , so chiral symmetry cannot be defined Two inequivalent representation of the algebra exist Parity anomaly C. Burden, A. N. Burkitt Lattice Fermions in Odd Dimensions Europhys. Lett., 3 (5), pp. 545-552 (1987) Starting from staggered formulation, analogous to the 4d case, shows that its continuum equivalent are flavors of components spinors. Parity symmetry is recovered by using both representations A set of chiral symmetries can be defined.

3. A. Bashir, Ma. de Jesus Anguiano Galicia Fermions in odd space-time dimensions: back to basics Few-Body Systems 0, 1–8 (2008), hep-ph/0502089v1 They show that it is possible to write a formulation of odd dimensional fermions using the fundamental representation of the Clifford algebra. The massless action has more symmetry than the massive case. “We demonstrate that by taking into account both the inequivalent fundamental representations of the gamma matrices for odd number of space-time dimensions, the resulting Lagrangian is not only parity invariant but also that we can write out chiral transformations within the two-component description of the fermion spinors which mix the fields belonging to the different inequivalent representations.”