D-terms and D-strings in open string models
Albion Lawrence, John McGreevy
TL;DR
The paper analyzes Fayet–Iliopoulos D-terms in open string (D-brane) settings within Type II Calabi–Yau backgrounds. It provides a tree-level worldsheet argument showing FI D-terms decouple from closed-string N=2 vector multiplet moduli, and shows that one-loop FI corrections arise only for anomalous U(1)s where anomalies are canceled by a Green–Schwarz mechanism. In a local Type IIA model with D6-branes at SU(3) angles, the one-loop divergence is quadratic in the open-string channel and is interpreted as a closed-string tadpole that is canceled when tadpoles are canceled. The work identifies D-term cosmic strings in the supersymmetric phases as D4-branes ending on D6-branes, and uses N=1 dualities to relate these results to previous heterotic FI-term analyses, highlighting how D-terms contribute to inflationary scenarios and stringy cosmic string physics.
Abstract
We study the Fayet-Iliopoulos (FI) D-terms on D-branes in type II Calabi-Yau backgrounds. We provide a simple worldsheet proof of the fact that, at tree level, these terms only couple to scalars in closed string hypermultiplets. At the one-loop level, the D-terms get corrections only if the gauge group has an anomalous spectrum, with the anomaly cancelled by a Green-Schwarz mechanism. We study the local type IIA model of D6-branes at SU(3) angles and show that, as in field theory, the one-loop correction suffers from a quadratic divergence in the open string channel. By studying the closed string channel, we show that this divergence is related to a closed string tadpole, and is cancelled when the tadpole is cancelled. Next, we study the cosmic strings that arise in the supersymmetric phases of these systems in light of recent work of Dvali et. al. In the type IIA intersecting D6-brane examples, we identify the D-term strings as D4-branes ending on the D6-branes. Finally, we use N=1 dualities to relate these results to previous work on the FI D-term of heterotic strings.