Conclusions
We have found a physical scenario relating 3D SW theory to an abelian version of the Casson invariant Z of the infinite cyclic covering space M̃ 3+ of M 3+ . In physical language, the space M 3+ emerges as a complement of superconducting probes. Whereas in mathematical language, M 3+ emerges as a complement of a thicken knot used to construct the manifold M 3 via surgery. In low-energy limit, the both languages match due to the Higgs mechanism generated by the scalar curvature R. Moreover, the partition function Z has been shown to be equivalent to the Alexander “polynomial” of M 3, which in principle, is related to topological torsion. 6
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Broda, B. (2002). Topological Contents of 3D Seiberg-Witten Theory. In: Damgaard, P.H., Jurkiewicz, J. (eds) New Developments in Quantum Field Theory. NATO Science Series: B:, vol 366. Springer, Boston, MA. https://doi.org/10.1007/0-306-47075-6_19
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DOI: https://doi.org/10.1007/0-306-47075-6_19
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