Topological phase, spin Chern-Simons theory and level rank duality on lens space

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.

36 pages, no figures

References in corpus (10)

• Level/rank Duality and Chern-Simons-Matter Theories
• Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• Exact results on ABJ theory and the refined topological string
• Classification of abelian spin Chern-Simons theories
• Reshetikhin-Turaev invariants of Seifert 3-manifolds for classical simple Lie algebras, and their asymptotic expansions
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Level-Rank Duality in Chern-Simons Theory from a Non-Supersymmetric Brane Configuration
• Level-rank duality of SU(2)k Chern-Simons theory, and of hypergraph and magic states
• Level-rank duality of knot and link invariants