The character of the supersymmetric Casimir energy

Dario Martelli; James Sparks

doi:10.1007/JHEP08(2016)117

The character of the supersymmetric Casimir energy

Dario Martelli, James Sparks

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Abstract

We study the supersymmetric Casimir energy E susy of N = 1 backslashmathcalN=1 field theories with an R-symmetry, defined on rigid supersymmetric backgrounds S 1 texttimesM 3, using a Hamiltonian formalism. These backgrounds admit an ambi-Hermitian geometry, and we show that the net contributions to E susy arise from certain twisted holomorphic modes on ℝthinspacetexttimes M 3, with respect to both complex structures. The supersymmetric Casimir energy may then be identified as a limit of an index-character that counts these modes. In particular this explains a recent observation relating E susy on S 1 texttimes S 3 to the anomaly polynomial. As further applications we compute E susy for certain secondary Hopf surfaces, and discuss how the index-character may also be used to compute generalized supersymmetric indices.

Original language	English
Pages (from-to)	1-39
Number of pages	39
Journal	Journal of High Energy Physics
Volume	2016
Issue number	8
Early online date	22 Aug 2016
DOIs	https://doi.org/10.1007/JHEP08(2016)117
Publication status	E-pub ahead of print - 22 Aug 2016

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The character of the supersymmetric_MARTELLI_Accepted 8Aug2016_GOLD VoRFinal published version, 533 KBLicence: CC BY

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abstract = "We study the supersymmetric Casimir energy E susy of N = 1 backslashmathcalN=1 field theories with an R-symmetry, defined on rigid supersymmetric backgrounds S 1 texttimesM 3, using a Hamiltonian formalism. These backgrounds admit an ambi-Hermitian geometry, and we show that the net contributions to E susy arise from certain twisted holomorphic modes on ℝthinspacetexttimes M 3, with respect to both complex structures. The supersymmetric Casimir energy may then be identified as a limit of an index-character that counts these modes. In particular this explains a recent observation relating E susy on S 1 texttimes S 3 to the anomaly polynomial. As further applications we compute E susy for certain secondary Hopf surfaces, and discuss how the index-character may also be used to compute generalized supersymmetric indices.",

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N2 - We study the supersymmetric Casimir energy E susy of N = 1 backslashmathcalN=1 field theories with an R-symmetry, defined on rigid supersymmetric backgrounds S 1 texttimesM 3, using a Hamiltonian formalism. These backgrounds admit an ambi-Hermitian geometry, and we show that the net contributions to E susy arise from certain twisted holomorphic modes on ℝthinspacetexttimes M 3, with respect to both complex structures. The supersymmetric Casimir energy may then be identified as a limit of an index-character that counts these modes. In particular this explains a recent observation relating E susy on S 1 texttimes S 3 to the anomaly polynomial. As further applications we compute E susy for certain secondary Hopf surfaces, and discuss how the index-character may also be used to compute generalized supersymmetric indices.

AB - We study the supersymmetric Casimir energy E susy of N = 1 backslashmathcalN=1 field theories with an R-symmetry, defined on rigid supersymmetric backgrounds S 1 texttimesM 3, using a Hamiltonian formalism. These backgrounds admit an ambi-Hermitian geometry, and we show that the net contributions to E susy arise from certain twisted holomorphic modes on ℝthinspacetexttimes M 3, with respect to both complex structures. The supersymmetric Casimir energy may then be identified as a limit of an index-character that counts these modes. In particular this explains a recent observation relating E susy on S 1 texttimes S 3 to the anomaly polynomial. As further applications we compute E susy for certain secondary Hopf surfaces, and discuss how the index-character may also be used to compute generalized supersymmetric indices.

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DO - 10.1007/JHEP08(2016)117

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JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

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ER -

The character of the supersymmetric Casimir energy

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