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In this work, we study the spontaneous Lorentz symmetry breaking due to an antisymmetric 2-tensor field in Minkowski spacetime. For a smooth quadratic potential, the spectrum of the theory exhibits massless and massive excitations. We show that the equations of motion for the free field obey some constraints which lead to the massive mode being nonpropagating at leading order. Besides, there exists a massless mode in the theory which can be identified with the usual Kalb-Ramond field, carrying only one on-shell degree of freedom. The same conclusion holds when one analyses the pole structure of its Feynman propagator. A new complete set of spin-type operators is found, which was the requirement to evaluate the propagator of the Kalb-Ramond field modified by the presence of a nonzero vacuum expectation value responsible for the Lorentz violation. [ABSTRACT FROM AUTHOR]

We proposed a six-dimensional string-like braneworld built from a warped product between a 3-brane and the Hamilton cigar soliton space, the stringcigar braneworld. This transverse manifold is a well-known steady solution of the Ricci flow equation that describes the evolution of a manifold. The resulting bulk is an interior and exterior metric for a thick string. Furthermore, the source satisfies the dominant energy condition. It is possible to realize the geometric flow as a result of variations of the matter content of the brane, actually, as its tensions. Furthermore, the Ricci flow defines a family of stringlike branes and we studied the effects that the evolution of the transverse space have on the geometric and physical quantities. The geometric flow makes the cosmological constant and the relationship between the Planck masses evolves. The gravitational massless mode remains trapped to the brane and the width of themode depends on the evolution parameter. For the Kaluza-Klein modes, the asymptotic spectrum of mass is the same as that for the thin string-like brane and the analogue Schrodinger potential also changes according to the flow. [ABSTRACT FROM AUTHOR]

It is shown that the results of our paper are correct, although the use of the chirality operator γ5 = σ1 in the paper is not correct, as fairly the authors of the comment stated. [ABSTRACT FROM AUTHOR]