Abstract
In this paper, we formulate a theory of the second-rank antisymmetric (pseudo)tensor field minimally coupled to a spinor, calculate the one-loop effective potential of the (pseudo)tensor field, and, explicitly, demonstrate that it is positively defined and possesses a continuous set of minima, both for tensor and pseudotensor cases. Therefore, our model turns out to display the dynamical Lorentz symmetry breaking. We also argue that, contrarily to the derivative coupling we use here, derivative-free couplings of the antisymmetric tensor field to a spinor do not generate the positively defined potential and thus do not allow for the dynamical Lorentz symmetry breaking.
Highlights
Lorentz symmetry breaking can be introduced in three manners: the explicit one, where the constant vector or tensor introducing the privileged spacetime direction is added from the very beginning; the anomalous one, where the spacetime possesses nontrivial topology allowing for a natural appearing of Lorentzbreaking terms; and the spontaneous one, where the constant vector or tensor emerges as a vacuum expectation of some vector or tensor field, respectively
We have successfully generalized the mechanism of the dynamical Lorentz symmetry breaking for theories of the second-rank antisymmetric tensor and pseudotensor fields; i.e., for the first time, we have generated the tensor bumblebee action as a quantum correction, while, earlier, only the vector bumblebee model was studied within the perturbative methodology
It is natural to expect that our results can open the way for further studies of spontaneous Lorentz symmetry breaking for generic dynamical tensor fields
Summary
Lorentz symmetry breaking can be introduced in three manners: the explicit one, where the constant vector or tensor introducing the privileged spacetime direction is added from the very beginning; the anomalous one, where the spacetime possesses nontrivial topology allowing for a natural appearing of Lorentzbreaking terms; and the spontaneous one, where the constant vector or tensor emerges as a vacuum expectation of some vector or tensor field, respectively. While the first manner became paradigmatic, being used to formulate the Lorentz-breaking extension of the standard model [1,2], and the second one allowed for a new, very interesting mechanism of the arising of the Carroll-Field-Jackiw (CFJ) term, essentially involving the nonperturbative methodology [3,4], interest in the third, spontaneous manner, is based on the fact that this approach provides a mechanism allowing us to explain the origin of Lorentz symmetry breaking. The first vector field theory model, involving a potential allowing for spontaneous Lorentz symmetry breaking, was introduced in [7]. We observe that only our coupling iψ Bμνγ1⁄2μ∂νγq5ψ allows us to obtain a potential for Bμν, while the other ones yield contributions depending on the stress tensor only, which justifies our choice of this coupling for the study of dynamical Lorentz symmetry breaking.
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