Gravity-induced instability of an electron on the D-3-brane

Abstract

We study the effect of gravity on stability of an electron living on the 3-brane. Our recently proposed fermion self-energy model is augmented by the energy of self-gravitating electron. This energy is evaluated using the gravitational field of a spherical source on the 3-brane derived by Garriga and Tanaka. Owing to the smallness of the electron radius, the short-range correction to this field dominates the Newtonian gravitational field of the electron. The magnitude of the short-range correction is proportional to the square of the curvature radius, $l$, of the anti-de Sitter space. On increasing $l$ beyond a critical value $l_c$, the equilibrium radius of the electron, undergoes a transition to a region where it becomes complex-signaling an instability of the electron. For the gravity-modified fermion self-energy model, we find $l_c=2\times 10^{-21}$ cm. If the electron is confined by the "hedgehog" potential, the critical length is $l_c=1.6\times 10^{-12}$ cm.

8 pages