Thresholds for Intersecting D-branes Revisited

TL;DR

Thresholds for Intersecting D-branes Revisited addresses one-loop gauge threshold corrections for intersecting D6-branes on toroidal orbifolds, focusing on infrared contributions from massless open-string states and tadpole-induced ultraviolet divergences. The authors apply two regularisation schemes—tree-channel dimensional regularisation and loop-channel zeta-function regularisation—to derive a running form $1/g_a^2(cmu) = 1/g_{string}^2 + (b_a/(16\pi^2))\ln(M_s^2/\mu^2) + \Delta_a$ and explicit ${\cal N}=1$ sector expressions for the threshold $\Delta_a$; they compare to Lust:2003ky and attribute differences to the treatment of light open-string states. They show that the two regularisation methods agree for the ${\cal N}=1$ sectors and that discrepancies with Lust arise from infrared subtraction choices, while also clarifying non-holomorphy in the moduli dependence and the role of light states. The work thus sharpens the understanding of gauge thresholds in intersecting-brane constructions and highlights the regularisation subtleties involved.

Abstract

Gauge threshold corrections for intersecting D6-brane string models on toroidal orbifold backgrounds are reconsidered. Both by dimensionally regularising the appearing open string one-loop diagrams in tree-channel as well as by zeta-function regularisation of the corresponding loop-channel one-loop diagrams, we arrive at a result which takes into account the infrared divergence from the contribution of the massless states in the running of the gauge coupling constant as well as the contribution of states, which become light in certain regions of the moduli space.