Tadpole Resummations in String Theory

TL;DR

This paper investigates whether resumming NS-NS tadpoles in string theory can recover true physical quantities, demonstrating that certain vacuum energies are exactly canceled by tadpole resummation, aligning with string field theory and Sen's conjecture.

Contribution

It provides a method to resum NS-NS tadpoles in string models, showing how this approach recovers the true vacuum energy and clarifies the effects of tadpoles in broken supersymmetry models.

Findings

Positive vacuum energy of Dp-branes is canceled by tadpole resummation.

Unoriented bosonic open-string theory's vacuum energy remains unchanged by tadpole resummation.

Tadpole resummation aligns with string field theory and Sen's conjecture.

Abstract

While R-R tadpoles should be canceled for consistency, string models with broken supersymmetry generally have uncanceled NS-NS tadpoles. Their presence signals that the background does not solve the field equations, so that these models are in "wrong" vacua. In this letter we investigate, with reference to some prototype examples, whether the true values of physical quantities can be recovered resumming the NS-NS tadpoles, hence by an approach that is related to the analysis based on String Field Theory by open-closed duality. We show that, indeed, the positive classical vacuum energy of a Dp-brane of the bosonic string is exactly canceled by the negative contribution arising from tree-level tadpole resummation, in complete agreement with Sen's conjecture on open-string tachyon condensation and with the consequent analysis based on String Field Theory. We also show that the vanishing classical vacuum energy of the SO(8192) unoriented bosonic open-string theory does not receive any tree-level corrections from the tadpole resummation. This result is consistent with the fact that this (unstable) configuration is free from tadpoles of massless closed-string modes, although there is a tadpole of the closed string tachyon. The application of this method to superstring models with broken supersymmetry is also discussed.