Chiral tensor fields and spontaneous breaking of Lorentz symmetry
arXiv:0712.3405 · doi:10.1142/S0217751X08041347
Abstract
Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric tensor fields. Fluctuations of the top quark drive the corresponding running coupling to a negative value as the renormalization scale is lowered. This may indicate a non-vanishing expectation value of the tensor field, and thus a spontaneous breaking of Lorentz invariance. Settling this issue will need the inclusion of tensor loops.
15 pages, 4 figures