Interactions in Intersecting Brane Models

TL;DR

This work analyzes tree-level three- and four-point amplitudes for open strings localized at D-brane intersections in Type II string theory. Using conformal field theory, it disentangles the classical (worldsheet instanton) and quantum (twist-field) contributions to three- and four-point functions, revealing how Yukawa couplings and flavour-changing neutral currents arise in intersecting brane models. In the four-point case, the authors show that the field-theory limit corresponds to exchanges of Kaluza-Klein modes, string oscillator states, and stretched heavy string modes, with a natural string-scale UV regulation of divergences. The results constrain flavor physics in these setups and point to extensions to more complex brane configurations and compactifications with potential implications for realistic SM-like constructions.

Abstract

We discuss tree level three and four point scattering amplitudes in type II string models with matter fields localized at the intersections of D-brane wrapping cycles. Using conformal field theory techniques we calculate the four fermion amplitudes. These give "contact" interactions that can lead to flavour changing effects. We show how in the field theory limit the amplitudes can be interpreted as the exchange of Kaluza-Klein excitations, string oscillator states and stretched heavy string modes.

Figures (10)

• Figure 1: intersections at right angles
• Figure 2: The images for branes at $\pi /3$, where $\rho =e^{2\pi i/3}$.
• Figure 3: A 'twisted' open string state
• Figure 4: three point interaction
• Figure 5: Transporting $X(z,\bar{z})$ around two twist fields