Lost chapters in CHL black holes: untwisted quarter-BPS dyons in the ℤ2 model

Fabian Fischbach (Bethe Center for Theoretical Physics, Universität Bonn, Bonn, D-53115, Germany) ; Albrecht Klemm (Bethe Center for Theoretical Physics, Universität Bonn, Bonn, D-53115, Germany; Hausdorff Center for Mathematics, Universität Bonn, Bonn, D-53115, Germany) ; Christoph Nega (Bethe Center for Theoretical Physics, Universität Bonn, Bonn, D-53115, Germany)

Motivated by recent advances in Donaldson-Thomas theory, four-dimensional N $$ \mathcal{N} $$ = 4 string-string duality is examined in a reduced rank theory on a less studied BPS sector. In particular we identify candidate partition functions of “untwisted” quarter-BPS dyons in the heterotic ℤ2 CHL model by studying the associated chiral genus two partition function, based on the M-theory lift of string webs argument by Dabholkar and Gaiotto. This yields meromorphic Siegel modular forms for the Iwahori subgroup B(2) ⊂ Sp4(ℤ) which generate BPS indices for dyons with untwisted sector electric charge, in contrast to twisted sector dyons counted by a multiplicative lift of twisted-twining elliptic genera known from Mathieu moonshine. The new partition functions are shown to satisfy the expected constraints coming from wall-crossing and S-duality symmetry as well as the black hole entropy based on the Gauss-Bonnet term in the effective action. In these aspects our analysis confirms and extends work of Banerjee, Sen and Srivastava, which only addressed a subset of the untwisted sector dyons considered here. Our results are also compared with recently conjectured formulae of Bryan and Oberdieck for the partition functions of primitive DT invariants of the CHL orbifold X = (K3 × T 2)/ℤ2, as suggested by string duality with type IIA theory on X.

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      "source": "Springer", 
      "value": "Motivated by recent advances in Donaldson-Thomas theory, four-dimensional   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 4 string-string duality is examined in a reduced rank theory on a less studied BPS sector. In particular we identify candidate partition functions of \u201cuntwisted\u201d quarter-BPS dyons in the heterotic \u21242 CHL model by studying the associated chiral genus two partition function, based on the M-theory lift of string webs argument by Dabholkar and Gaiotto. This yields meromorphic Siegel modular forms for the Iwahori subgroup B(2) \u2282 Sp4(\u2124) which generate BPS indices for dyons with untwisted sector electric charge, in contrast to twisted sector dyons counted by a multiplicative lift of twisted-twining elliptic genera known from Mathieu moonshine. The new partition functions are shown to satisfy the expected constraints coming from wall-crossing and S-duality symmetry as well as the black hole entropy based on the Gauss-Bonnet term in the effective action. In these aspects our analysis confirms and extends work of Banerjee, Sen and Srivastava, which only addressed a subset of the untwisted sector dyons considered here. Our results are also compared with recently conjectured formulae of Bryan and Oberdieck for the partition functions of primitive DT invariants of the CHL orbifold X = (K3 \u00d7 T 2)/\u21242, as suggested by string duality with type IIA theory on X."
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Published on:
25 January 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 1
Pages 1-68
DOI:
https://doi.org/10.1007/JHEP01(2021)157
arXiv:
2005.07712
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: