String k-anomalies and D=10 Supergravity constraints: the solution of a puzzle

TL;DR

This paper resolves a discrepancy between two methods of deriving superspace constraints in D=10 supergravity, confirming their consistency and advancing understanding of superstring anomaly cancellation.

Contribution

It demonstrates the reconciliation of recent superspace constraints with previous solutions, clarifying the impact of the $$--anomaly cancellation mechanism.

Findings

Confirmed agreement between different superspace constraint derivations

Resolved a longstanding puzzle in D=10 supergravity

Enhanced understanding of superstring anomaly cancellation

Abstract

The $\kappa$--anomaly cancellation mechanism in the heterotic superstring determines the superspace constraints for N=1, D=10 Supergravity--Super--Yang--Mills theory. We point out that the constraints found recently in this way appear to disagree with superspace solutions found in the past. We solve this puzzle establishing perfect agreement between the two methods.