On tadpoles and vacuum redefinitions in String Theory
E. Dudas, G. Pradisi, M. Nicolosi, A. Sagnotti
TL;DR
The paper investigates how NS-NS tadpoles, which arise with supersymmetry breaking in string theory, complicate the definition of a stable background and drive infrared divergences. It develops a perturbative framework based on expansions around a wrong Minkowski vacuum, using field-theory toy models to study resummation flows toward nearby extrema and to identify conditions under which the series converges or terminates. The authors provide explicit string-theory examples where vacuum redefinitions relate different orientifolds (notably a type II orientifold with NS-NS tadpoles to a type-0 orientifold) and show that one-loop threshold corrections can be UV finite in many non-supersymmetric constructions, with decoupling of tadpoles from transverse moduli in higher codimensions. They also discuss the limitations of the approach at higher orders and emphasize the need for Dyson-like resummations beyond genus 3/2, outlining avenues for future work in implementing vacuum redefinitions in full string theory.
Abstract
Tadpoles accompany, in one form or another, all attempts to realize supersymmetry breaking in String Theory, making the present constructions at best incomplete. Whereas these tadpoles are typically large, a closer look at the problem from a perturbative viewpoint has the potential of illuminating at least some of its qualitative features in String Theory. A possible scheme to this effect was proposed long ago by Fischler and Susskind, but incorporating background redefinitions in string amplitudes in a systematic fashion has long proved very difficult. In the first part of this paper, drawing from field theory examples, we thus begin to explore what one can learn by working perturbatively in a ``wrong'' vacuum. While unnatural in Field Theory, this procedure presents evident advantages in String Theory, whose definition in curved backgrounds is mostly beyond reach at the present time. At the field theory level, we also identify and characterize some special choices of vacua where tadpole resummations terminate after a few contributions. In the second part we present a notable example where vacuum redefinitions can be dealt with to some extent at the full string level, providing some evidence for a new link between IIB and 0B orientifolds. We finally show that NS-NS tadpoles do not manifest themselves to lowest order in certain classes of string constructions with broken supersymmetry and parallel branes, including brane-antibrane pairs and brane supersymmetry breaking models, that therefore have UV finite threshold corrections at one loop.