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We revisit the proposal of arXiv:2104.05716 for the worldsheet description ofstring theory compactifications on special holonomy manifolds obtained viaconnected sums: the geometric construction corresponds to a diamond ofinclusions of worldsheet algebras. We present new evidence for the proposal byconsidering compactifications on the Schoen Calabi-Yau manifold.

Superconformal algebras for the Schoen Calabi-Yau manifold