Anomalies & Tadpoles

TL;DR

This work establishes a general framework linking massless RR tadpoles in open/unoriented string vacua to anomalies across all even dimensions, without assuming target-space supersymmetry. By analyzing the odd-spin sector and using modular invariance, it identifies a precise mapping: sectors with non-zero Witten index ${\cal I}_{i}$ correspond to irreducible anomalies via tadpoles, while sectors with ${\cal I}_{i}=0$ reveal anomalous amplitudes only through higher-point insertions. The authors show that tadpole cancellation enforces the cancellation of irreducible anomalies and that the remaining reducible anomalies factorize, unveiling a generalized Green-Schwarz mechanism with explicit WZ couplings between RR fields and boundary data $B^{i}_{a}$. They also extend the analysis to sectors with ${\cal I}=0$, showing how anomalous amplitudes with suitable insertions surface RR-tadpole information, and discuss implications for anomalous U(1) factors and non-supersymmetric vacua. Overall, the paper provides a topologically driven, model-independent dictionary between RR tadpoles and anomalies, applicable to broad open-string constructions and their dual descriptions, including non-geometric and non-supersymmetric settings.

Abstract

We show that massless RR tadpoles in vacuum configurations with open and unoriented strings are always related to anomalies. RR tadpoles arising from sectors of the internal SCFT with non-vanishing Witten index are in one-to-one correspondence with conventional irreducible anomalies. The anomalous content of the remaining RR tadpoles can be disclosed by considering anomalous amplitudes with higher numbers of external legs. We then provide an explicit parametrization of the anomaly polynomial in terms of the boundary reflection coefficients, i.e. one-point functions of massless RR fields on the disk. After factorization of the reducible anomaly, we extract the relevant WZ couplings in the effective lagrangians.