Kavli Affiliate: Jeffrey A. Harvey
| First 5 Authors: Jeffrey A. Harvey, Tai Wai Hu, , ,
| Summary:
Compactification of heterotic string on a Calabi-Yau threefold can lead to a
four-dimensional low-energy effective theory which contains a $U(1)$ gauge
theory which is pseudo-anomalous, meaning that the fermion content is
anomalous, but that the fermion anomaly is cancelled by a four-dimensional
version of the Green-Schwarz mechanism involving a shift of the
model-independent axion field. It is also well known that a field-dependent
Fayet-Iliopoulos like term is induced at one-loop in string perturbation theory
in such compactifications and that this leads to a mass for the $U(1)$ gauge
field. Explicit one-loop computations of the mass shifts of massless charged
scalars and fermions implied by this mechanism were originally carried out in
the 1980’s and have been revisited more recently using techniques of string
field theory and super Riemann surfaces. We consider such theories further
compactified on a circle of radius $R$. There is then an infinite tower of BPS
states with winding and momenta on the circle. BPS strings which wind the
circle can, at large $R$, be viewed as macroscopic or cosmic strings in four
spacetime dimensions, or, at generic $R$, as BPS states in three dimensions. We
compute the one-loop mass renormalization of such states and show that it is
nonzero and proportional to their pseudo-anomalous $U(1)$ charge.
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