Scalar Mass and Cosmological Constant induced by ``Anomalous" $U(1)$ $D$-term

TL;DR

This paper explores how anomalous $U(1)$ gauge symmetries in supersymmetric theories induce scalar masses and a positive cosmological constant via Fayet-Iliopoulos $D$-terms, with potential cancellations leading to universal scalar masses and zero cosmological constant.

Contribution

It demonstrates a mechanism where anomalous $U(1)$ $D$-terms contribute to scalar masses and cosmological constant, with natural realizations in string models and possible cancellations.

Findings

D-term contributions can generate scalar masses and positive cosmological constant.

In some models, F- and D-term contributions cancel, resulting in universal scalar masses and zero cosmological constant.

The mechanism is exemplified in a simple orbifold string model.

Abstract

When the supersymmetric theory contains the ``anomalous" $U(1)$ gauge symmetry with Green-Schwarz anomaly cancellation mechanism in 4 dimensions, its Fayet-Iliopoulos $D$-term generates non-universal scalar masses and the positive cosmological constant after the supersymmetry breaking. Both give the new contributions to the known results from $F$-term. Our mechanism is naturally realized in many string models and in some cases, leads to remarkable cancellations between $F$- and $D$-term contributions, providing the universal scalar mass and vanishing cosmological constant. We illustrate how such a possibility can arise by taking a simple orbifold example.