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- W2871931184 abstract "A bstract We study 3d $$ mathcal{N}=2 $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> supersymmetric gauge theories on closed oriented Seifert manifolds — circle bundles over an orbifold Riemann surface —, with a gauge group G given by a product of simply-connected and/or unitary Lie groups. Our main result is an exact formula for the supersymmetric partition function on any Seifert manifold, generalizing previous results on lens spaces. We explain how the result for an arbitrary Seifert geometry can be obtained by combining simple building blocks, the “fibering operators.” These operators are half-BPS line defects, whose insertion along the S 1 fiber has the effect of changing the topology of the Seifert fibration. We also point out that most supersymmetric partition functions on Seifert manifolds admit a discrete refinement, corresponding to the freedom in choosing a three-dimensional spin structure. As a strong consistency check on our result, we show that the Seifert partition functions match exactly across infrared dualities. The duality relations are given by intricate (and seemingly new) mathematical identities, which we tested numerically. Finally, we discuss in detail the supersymmetric partition function on the lens space L ( p, q ) b with rational squashing parameter b 2 ∈ ℚ, comparing our formalism to previous results, and explaining the relationship between the fibering operators and the three-dimensional holomorphic blocks." @default.
- W2871931184 created "2018-07-19" @default.
- W2871931184 creator A5027517013 @default.
- W2871931184 creator A5059565451 @default.
- W2871931184 creator A5066293538 @default.
- W2871931184 date "2018-11-01" @default.
- W2871931184 modified "2023-09-23" @default.
- W2871931184 title "Seifert fibering operators in 3d $$ mathcal{N}=2 $$ theories" @default.
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