We provide a general formula for the partition function of three-dimensional (formula presented) gauge theories placed on S2 ×S1 with a topological twist along S2, which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to Ω-backgrounds, as well as two-dimensional theories on S2 and four-dimensional theories on S2 × T2. In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants.

Benini, F., Zaffaroni, A. (2015). A topologically twisted index for three-dimensional supersymmetric theories. JOURNAL OF HIGH ENERGY PHYSICS, 2015(7), 77 [10.1007/JHEP07(2015)127].

A topologically twisted index for three-dimensional supersymmetric theories

Zaffaroni, A
2015

Abstract

We provide a general formula for the partition function of three-dimensional (formula presented) gauge theories placed on S2 ×S1 with a topological twist along S2, which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to Ω-backgrounds, as well as two-dimensional theories on S2 and four-dimensional theories on S2 × T2. In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants.
Articolo in rivista - Articolo scientifico
Chern-simons theories; Differential and algebraic geometry; Nonperturbative effects; Supersymmetry and Duality;
supersimmetria
English
2015
2015
7
77
127
partially_open
Benini, F., Zaffaroni, A. (2015). A topologically twisted index for three-dimensional supersymmetric theories. JOURNAL OF HIGH ENERGY PHYSICS, 2015(7), 77 [10.1007/JHEP07(2015)127].
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