Residue formulas for the large \(k\) asymptotics of Witten’s invariants of Seifert manifolds. The case of \(SU(2)\). (English) Zbl 0864.57017
The author studies the large \(k\) asymptotics of \(SU(2)\) Witten’s invariant of general Seifert manifolds \(X_{g,\{{p \over q}\}}\). He calculates all contributions \(Z^{(c)} (X_{g,\{{p\over q}\}};k)\) and relates them to connected components of the moduli space of flat connections. The contributions of irreducible connections are expressed in terms of intersection numbers of their moduli spaces. As a byproduct of calculations the author derives the full asymptotic expansion of the partition function of \(2d\) \(SU(2)\) Yang-Mills theory on a Riemann surface with punctures, including the contributions of constant curvature reducible connections. The alternative way of deriving the asymptotics of Witten’s invariants of Seifert manifolds which relates them to Kostant’s partition function is also discussed.
Reviewer: V.Abramov (Tartu)
MSC:
| 57N10 | Topology of general \(3\)-manifolds (MSC2010) |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
Keywords:
Chern-Simons action; topological field theory; Witten’s invariant; Seifert manifolds; moduli space; flat connections; intersection numbers; Yang-Mills theory; Riemann surfaceReferences:
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