Cosmic strings from pseudo-anomalous Fayet-Iliopoulos U(1)FI in D3/D7 brane inflation

We examine the consequences of recent developments on Fayet-Iliopoulos (FI) terms for D-term inflationary models. There is currently no known way to couple constant FI terms to supergravity consistently; only field-dependent FI terms are allowed. These are natural in string theory and we argue that the FI term in D3/D7 inflation turns out to be of this type, corresponding to a pseudo-anomalous U(1)_FI. The anomaly is canceled by the Green-Schwarz (GS) mechanism in 4 dimensions. Inflation proceeds as usual, except that the scale is set by the GS parameter δ_GS. Cosmic strings resulting from a pseudo-anomalous U(1) have potentially interesting characteristics. Originally expected to be global, they turn out to be local in the string theory context and can support currents. We outline the nature of these strings, discuss bounds on their formation, and summarize resulting cosmological consequences.