{"arxiv_id":"2104.14710","title":"Chern-Simons Invariants from Ensemble Averages","abstract":"We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice with integral quadratic form $Q$. We provide evidence that the holographic dual after the ensemble average is the three-dimensional Abelian Chern-Simons theory with kinetic term determined by $Q$. The resulting partition function can be written as a modular form, expressed as a sum over the partition functions of Chern-Simons theories on lens spaces. For odd lattices, the dual bulk theory is a spin Chern-Simons theory, and we identify several novel phenomena in this case. We also discuss the holographic duality prior to averaging in terms of Maxwell-Chern-Simons theories.","primary_cat":"hep-th","cross_cats":["math.NT"],"submitted_at":"2021-04-30T01:02:37+00:00","latest_version":2,"source":"arxiv","source_label":"arXiv","source_url":null,"has_pdf":true,"has_source":false,"verdict":"ACCEPT","confidence":"MODERATE","one_line_summary":"Averaging the partition function of a free-boson CFT over the moduli space of any indefinite integral lattice produces a Siegel-Eisenstein series that decomposes into Abelian Chern-Simons partition functions on lens spaces.","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","upvotes":0,"downvotes":0,"pith_score":0.0,"inbound_count":7,"_links":{"html":"https://pith.science/paper/2104.14710","verdict":"/api/v1/verdicts/2104.14710"}}