Bosonic fields in crystal manifold

Abstract

A chain-like or a 1D crystal-like universe made of intersecting membranes in extra dimensions in a Randall-Sundrum scenario is studied. A background gravitational metric satisfying the right boundary conditions is considered to study the localization of the scalar, gauge and Kalb-Ramond field. It is found that the wave function for the fields are Bloch waves. The mass modes equations are calculated allowing us to show the zero-gap mass behavior and the mass dispersion relation for each field. Finally we generalize all these results and consider q−forms in the crystal membrane universe. We show that, depending to the dimension D, the form q and the dilaton coupling λ the mass spectrum can be the same for the different bosonic field studied. 1

Gauge field localization on the brane through geometrical coupling

“…In a separate paper we consider this and show that the generalization to p-forms in more dimensions is possible. The main result is that the gauge field can emerge from the localization of the two form in five dimensions [11]. Another aspect to consider is the generalization to a non-abelian case as in [12] or to other couplings with the field strength [13].…”

Gauge field emergence from Kalb–Ramond localization

“…Therefore, the result obtained by them is not generally valid. A solution to this problem was found by the present authors in [42]. We show there that the choice ∂ μ A μ = A 5 = 0, yet being valid as a particular solution, is unnecessary.…”

“…Here we must review the results found by the authors in a previous work [42]. The geometrical coupling is proposed with action…”

“…Some authors have introduced a dilaton coupling in order to solve it [5] and other propose that a strongly coupled gauge theory in five dimensions can generate a massless photon in the brane [6]. Modifications of the model considering spherical branes, multiple branes or induced branes can be found in [7][8][9][10][11][12][13][14][15][16].…”

Massive p-form trapping as a p-form on a brane

“…It is important to point that in the models mentioned here the Hodge Duality is not valid since quadratic terms breaks this duality. The analysis of massive modes of p-forms has also been considered in the literature [22][23][24][25][26][27] After the work of RS several recent results have been developed based on the idea of thick membranes and its implications for brane-world physics [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. The advantage of these models is that the singularity generated by the brane is eliminated.…”