On Adler-Bell-Jackiw Anomaly in 3-brane Scenario

We investigate the ABJ anomaly in the framework of an effective field theory for a 3-brane scenario and show that the contribution from induced gravity on the brane depends on both the topological structure of the bulk space-time and the embedding of the brane in the bulk. This fact implies the existence of a non-trivial vacuum structure of bulk quantum gravity. Furthermore, we argue that this axial gravitational anomaly may not necessarily be cancelled by choosing the matter content on the brane since it could be considered as a possible effect from bulk quantum gravity. The idea that our observable space-time may be a (3+1)-dimensional topological defect of some higher dimensional quantum field theory has persisted over a number of years [1,2]. In this scenario, the observed elementary particles are the light particles trapped on the (3+1)-dimensional defect and the Standard Model (SM), which is believed to be the correct theory characterizing the interactions among these elementary particles, appears as a lowenergy effective theory of a more fundamental theory in higher dimensions. The exception is the graviton: it mediates the quantum gravitational interaction, and it can propagate in the whole bulk due to the equivalence between gravity and space-time geometry. Of course, it might be possible that some other particles such as heavy fermions – beyond the reach of present accelerators – also exist in the bulk space-time. It is remarkable that such exotic yet simple considerations can address some fundamental problems. For example, it provides an alternative mechanism for solving the hierarchy problem [4], in contrast to those that modify the SM itself such as technicolor and supersymmetric extensions. It also gives a natural explanation as to why gravitational interactions are much weaker than other forces [3], and it even gives an alternative means for addressing the cosmological problem [2,5]. This scenario has gained support from the application of the non-perturbative superstring theory. A physically realistic example is that an N = 1 SU(5) supersymmetric gauge theory with three generations of chiral matter fields can indeed come from one sector of type-I ∗E-mail: [email protected] †E-mail: [email protected]