We study an index for three-dimensional supersymmetric gauge theories placed on a sphere and immersed in external magnetic fields — in fact topologically twisted. We find an exact non-perturbative formula for this index, applying supersymmetric localization techniques. The index, different from the more common superconformal index, counts Landau-level ground states of the theories in magnetic field. It has physical applications: to the study of non-perturbative dualities, of moduli spaces, of Chern-Simons theory and Verlinde algebras, of wrapped branes in string theory and the quantum entropy of black holes; as well as mathematical applications: to quantum cohomology and its K-theoretic generalization.

A topologically twisted index for three-dimensional gauge theories / Benini, Francesco. - PART D: PARALLEL SESSIONS - Branes and Instantons in String Theory:(2018), pp. 4151-4156. (Intervento presentato al convegno Proceedings of the MG14 Meeting on General Relativity tenutosi a Rome nel 12-18 July 2015) [10.1142/9789813226609_0554].

A topologically twisted index for three-dimensional gauge theories

Benini, Francesco
2018-01-01

Abstract

We study an index for three-dimensional supersymmetric gauge theories placed on a sphere and immersed in external magnetic fields — in fact topologically twisted. We find an exact non-perturbative formula for this index, applying supersymmetric localization techniques. The index, different from the more common superconformal index, counts Landau-level ground states of the theories in magnetic field. It has physical applications: to the study of non-perturbative dualities, of moduli spaces, of Chern-Simons theory and Verlinde algebras, of wrapped branes in string theory and the quantum entropy of black holes; as well as mathematical applications: to quantum cohomology and its K-theoretic generalization.
2018
The Fourteenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories : proceedings of the MG14 Meeting on General Relativity, University of Rome "La Sapienza", Italy, 12-18 July 2015
PART D: PARALLEL SESSIONS - Branes and Instantons in String Theory
4151
4156
978-981-3226-59-3
978-981-322-660-9
10.1142/9789813226609_0554
http://www.worldscientific.com/doi/abs/10.1142/9789813226609_0554
World Scientific
Benini, Francesco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/67751
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