Presentation Holonomy in Chern–Simons Theory Flat line bundles over the 2–framing torsor and the framing anomaly
Presentation Holonomy in Chern–Simons Theory Flat line bundles over the 2–framing torsor and the framing anomaly
In the Witten–Reshetikhin–Turaev (WRT) formulation of Chern–Simons theory, the closed3–manifold invariant is not canonically a scalar: it depends on a choice of 2–framing. Equivalently, the partition function is a section of a one–dimensional complex vector space varyingover the Z–torsor F2(M) of 2–framings. We prove that the WRT partition function defines aflat unitary line bundle over F2(M), and that its holonomy under the canonical generator isexp 2πi 24 c(G,k), where c(G,k) is the WZW central charge. We state a precise theorem at the level of WRTTQFT and record the SU(2)k check on S3 in terms of the modular data (S,T).
theoretical physics, central charge 𝑐 ( 𝐺 , 𝑘 ) c(G,k), topological quantum field theory, 2-framing torsor, Chern–Simons theory, 3-manifolds, framing anomaly, surgery presentation, flat unitary line bundle, anomalies, WZW model, invertible field theory, holonomy, quantum field theory, central charge 𝑐 ( 𝐺 , 𝑘 ) c(G,k), symmetry
theoretical physics, central charge 𝑐 ( 𝐺 , 𝑘 ) c(G,k), topological quantum field theory, 2-framing torsor, Chern–Simons theory, 3-manifolds, framing anomaly, surgery presentation, flat unitary line bundle, anomalies, WZW model, invertible field theory, holonomy, quantum field theory, central charge 𝑐 ( 𝐺 , 𝑘 ) c(G,k), symmetry
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