Anomaly Cancellations in the Type I D9-anti-D9 System and the USp(32) String Theory

TL;DR

The paper analyzes the non-supersymmetric Type I D9–D${\bar{9}}$ system and shows that gravitational and gauge anomalies cancel via a Green–Schwarz mechanism when $n-m=32$, with a dual $USp(n)\times USp(m)$ solution also consistent with anomaly constraints.Tachyon dynamics and couplings are incorporated, demonstrating how tachyon condensation reduces the system to a tachyon-free $USp(32)$ theory, which deliberately lacks spacetime supersymmetry.String-theoretic analyses of open-string spectra and RR-tadpoles corroborate the EFT results, establishing the same anomaly-cancellation conditions and extending them to the $USp$-type case, while clarifying the role of RR boundary signs and world-sheet cuts.The work provides a general framework for D9–D${\bar{9}}$ pairs in string theory, showing that anomaly cancellation requires specific relations between $n$ and $m$ (e.g., $n-m=32$ or $m-n=32$ depending on the projection) and outlining the implications for the spectrum and D-brane content in the resulting theories.The discussion of the $USp(32)$ theory highlights its non-supersymmetric nature, the presence of NS-NS tadpoles, and potential connections to heterotic constructions, suggesting rich structural links between KO/KSp/K-theory classifications and non-supersymmetric string vacua.

Abstract

We check some consistency conditions for the D9-anti-D9 system in type I string theory. The gravitational anomaly and gauge anomaly for SO(n) x SO(m) gauge symmetry are shown to be cancelled when n-m=32. In addition, we find that a string theory with USp(n) x USp(m) gauge symmetry also satisfies the anomaly cancellation conditions. After tachyon condensation, the theory reduces to a tachyon-free USp(32) string theory, though there is no spacetime supersymmetry.