Topological phase, spin Chern-Simons theory and level rank duality on lens space
arXiv:2108.09300 · doi:10.1007/JHEP04(2022)074
Abstract
We study a method to compute a topological phase factor of partition function for pure Chern-Simons theory incorporating the supersymmetric localization. We develop a regularization preserving supersymmetry and the topological phase appears as a result of the supersymmetric regularization. Applying this method to pure Chern-Simons theory on lens space we compute the background dependent phase factor coming from the Chern-Simons term. We confirm that the partition function computed in this method enjoys a couple of level rank dualities including the one recently proposed in arXiv:1607.07457 for all ranks and levels within our numerical calculation. We also present a phase factor with which the lens space partition function exhibits the perfect match between any level rank dual pair including the total phase.
arXiv comment36 pages, no figures
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