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BPS invariants for Seifert manifolds. (English) Zbl 1435.81195

Summary: We calculate the homological blocks for Seifert manifolds from the exact expression for the \(G = \mathrm{SU}(N)\) Witten-Reshetikhin-Turaev invariants of Seifert manifolds obtained by Lawrence, Rozansky, and Mariño. For the \(G = \mathrm{SU}(2)\) case, it is possible to express them in terms of the false theta functions and their derivatives. For \(G = \mathrm{SU}(N) \), we calculate them as a series expansion and also discuss some properties of the contributions from the abelian flat connections to the Witten-Reshetikhin-Turaev invariants for general \(N\). We also provide an expected form of the \(S\)-matrix for general cases and the structure of the Witten-Reshetikhin-Turaev invariants in terms of the homological blocks.

MSC:

81T45 Topological field theories in quantum mechanics
58J28 Eta-invariants, Chern-Simons invariants
81T60 Supersymmetric field theories in quantum mechanics
81U20 \(S\)-matrix theory, etc. in quantum theory
53Z05 Applications of differential geometry to physics
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References:

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