{"arxiv_id":"hep-th/0601068","title":"Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory","abstract":"We study Chern-Simons theory on 3-manifolds $M$ that are circle-bundles over 2-dimensional surfaces $\\Sigma$ and show that the method of Abelianisation, previously employed for trivial bundles $\\Sigma \\times S^1$, can be adapted to this case. This reduces the non-Abelian theory on $M$ to a 2-dimensional Abelian theory on $\\Sigma$ which we identify with q-deformed Yang-Mills theory, as anticipated by Vafa et al. We compare and contrast our results with those obtained by Beasley and Witten using the method of non-Abelian localisation, and determine the surgery and framing presecription implicit in this path integral evaluation. We also comment on the extension of these methods to BF theory and other generalisations.","primary_cat":"hep-th","cross_cats":[],"submitted_at":"2006-01-11T13:06:17+00:00","latest_version":2,"source":"arxiv","source_label":"arXiv","source_url":null,"has_pdf":true,"has_source":false,"verdict":"ACCEPT","confidence":"HIGH","one_line_summary":"Abelianisation of Chern-Simons theory on non-trivial circle bundles over surfaces reduces it to q-deformed Yang-Mills, with partition function a sum of WZW modular matrices weighted by T^{-p}.","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","upvotes":0,"downvotes":0,"pith_score":0,"inbound_count":17,"_links":{"html":"https://pith.science/paper/hep-th/0601068","verdict":"/api/v1/verdicts/hep-th/0601068"}}