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We argue that instanton partition functions of N=2 gauge theories in the presence of a surface operator can also be computed from the corresponding W-algebra. We test this proposal by analysing the Polyakov-Bershadsky W_3^(2) algebra obtaining results that are in agreement with the known partition functions for SU(3) gauge theories with a so called s"},"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":"1011.0289","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-11-01T11:03:46Z","cross_cats_sorted":[],"title_canon_sha256":"02f235cf8015bfb4afdee27b28f2f7952e3e41a77139ec9a10d5c59988f89ee0","abstract_canon_sha256":"5c3f02a88892bb5702ae6870543a8bc5c3d35fbc29358f79e2f67a9a2fd4b48c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:49.076679Z","signature_b64":"ISywWF+WMn3wa3kEbIMV8kDHn0+0h92DmwfzuekHgTFiJOa6fMQFf2PYv67pWThefOxzWaUNbzDzREp/LgR8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c2eb88e93f511118381f94c8cb7ba15d0c6d4e9e45ab9ee83067a3931fba235","last_reissued_at":"2026-05-18T04:25:49.076075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:49.076075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"W-algebras and surface operators in N=2 gauge theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Niclas Wyllard","submitted_at":"2010-11-01T11:03:46Z","abstract_excerpt":"A general class of W-algebras can be constructed from the affine sl(N) algebra by (quantum) Drinfeld-Sokolov reduction and are classified by partitions of N. 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