More Modular Invariant Anomalous U(1) Breaking

TL;DR

This paper develops a formalism for analyzing the breaking of multiple anomalous U(1) symmetries in supergravity, focusing on modular invariance, effective superpotentials, and implications for string models.

Contribution

It introduces a superfield redefinition approach to account for vector multiplet exchange and modular weight shifts in theories with multiple anomalous U(1)s.

Findings

Modular weights of light fields are shifted, preserving modular invariance.

Effective superpotential includes operators relevant for proton decay.

Formalism extends to Green-Schwarz mechanism in string constructions.

Abstract

We consider the case of several scalar fields, charged under a number of U(1) factors, acquiring vacuum expectation values due to an anomalous U(1). We demonstrate how to make redefinitions at the superfield level in order to account for tree-level exchange of vector supermultiplets in the effective supergravity theory of the light fields in the supersymmetric vacuum phase. Our approach builds upon previous results that we obtained in a more elementary case. We find that the modular weights of light fields are typically shifted from their original values, allowing an interpretation in terms of the preservation of modular invariance in the effective theory. We address various subtleties in defining unitary gauge that are associated with the noncanonical Kahler potential of modular invariant supergravity, the vacuum degeneracy, and the role of the dilaton field. We discuss the effective superpotential for the light fields and note how proton decay operators may be obtained when the heavy fields are integrated out of the theory at the tree-level. We also address how our formalism may be extended to describe the generalized Green-Schwarz mechanism for multiple anomalous U(1)'s that occur in four-dimensional Type I and Type IIB string constructions.