Proton Decay in Intersecting D-brane Models

TL;DR

This paper investigates proton decay via dimension-six operators in a class of intersecting D-brane GUT-like models derived from Type IIA string theory. It computes the 4-fermion amplitude from disk worldsheet with twist-field correlators, revealing a universal scaling with $\alpha_{GUT}^{-1/3}$ relative to four-dimensional GUTs. After including threshold corrections associated with the Ray-Singer torsion $L(Q)$, the net enhancement remains modest. Numerical evaluation of the twist integral $I(\theta_1,\theta_2,\theta_3)$ yields values in the range about 7–11.5 for plausible angles, and the resulting proton lifetime due to dimension-six operators remains near $10^{36}$ years, similar to SUSY GUT expectations. The work demonstrates the calculability of these effects in perturbative Type II string theory and highlights the role of compactification thresholds in proton decay predictions.

Abstract

We analyze proton decay via dimension six operators in certain GUT-like models derived from Type IIA orientifolds with $D6$-branes. The amplitude is parametrically enhanced by a factor of $α_{GUT}^{-1/3}$ relative to the coresponding result in four-dimensional GUT's. Nonetheless, even assuming a plausible enhancement from the threshold corrections, we find little overall enhancement of the proton decay rate from dimension six operators, so that the predicted lifetime from this mechanism remains close to $10^{36}$ years.