Intersecting Brane Worlds at One Loop

TL;DR

The paper develops a comprehensive framework to compute one-loop N-point amplitudes on intersecting D6-branes, enabling detailed study of Yukawa coupling renormalization and Kähler potential structure. It shows that leading divergences cancel due to RR tadpole cancellation in SUSY configurations, and that string-scale physics softens the conventional power-law running of Yukawas via the scalar propagator $\Pi(k^2)$. A general method to extract $N$-point amplitudes, including cases without gauge-boson loops, is presented, with boundary-changing operators playing a central role. The results illuminate how stringy UV physics regulates field-theory running and establish new computational tools (annulus-only diagrams and boundary-changing operator formalism), while outlining open issues in Möbius-strip contributions and full divergence cancellation.

Abstract

We develop techniques for one-loop diagrams on intersecting branes. The one-loop propagator of chiral intersection states on D6 branes is calculated exactly and its finiteness is shown to be guaranteed by RR tadpole cancellation. The result is used to demonstrate the expected softening of power law running of Yukawa couplings at the string scale. We also develop methods to calculate arbitrary N-point functions at one-loop, including those without gauge bosons in the loop. These techniques are also applicable to heterotic orbifold models.

Figures (3)

• Figure 1: An annulus contribution to 3 point functions.
• Figure 2: Feynman diagrams in the field theory equivalent to our limit; we have factorised onto the scalar propagator, and consider only gauge and self-couplings.
• Figure 3: A linear plot of the "running" Yukawa coupling in modular parameter $t$, lower graph. The peak is very close to $t=1$, i.e. the string scale. The top graph is the standard power-law behaviour continued. The middle graph is the field theory approximation using string improved propagators as defined in the text.