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These compactifications generalize the example of the heterotic string on $K3\\times T^2$ studied in the context of dualities in ${\\cal N}=2$ string theories. We evaluate the new supersymmetric index for these theories and show that their expansion can written in terms of the McKay-Thompson series associated with the $\\mathbb{Z}_N$ involution embedd"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.05425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-19T11:08:24Z","cross_cats_sorted":[],"title_canon_sha256":"8c0a74a67143c09cfc779a39c18c07be0f225ef1848c95234f19d69104f11750","abstract_canon_sha256":"9d7fe229c55294a97cc9301d941e6bf567d7f9cddbf60d37b763be0df9005839"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:31.237474Z","signature_b64":"udMBpzLC/eo78DCKApDrIKm45InMR7KwHHK2A+aFE/vEnYn65S4QKQyVVH9nw2qQh/Tm2LijixMPWl7TbmSKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50d0873a471ca27ebb09a7a2110f80ede6d1d3e7bd7948c95b0739b7f52d3c37","last_reissued_at":"2026-05-18T01:18:31.236905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:31.236905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heterotic string on the CHL orbifold of K3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Dieter Lust, Justin R. 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