Decomposition of denominator formulae of some BKM Lie superalgebras - II

Suresh Govindarajan (Department of Physics, Indian Institute of Technology Madras, Chennai, India) ; Mohammad Shabbir (The Institute of Mathematical Sciences, Chennai, India; Homi Bhabha National Institute, Training School Complex, Mumbai, India)

The square-root of Siegel modular forms of CHL ZN orbifolds of type II compactifications are denominator formulae for some Borcherds-Kac-Moody Lie superalgebras for N=1,2,3,4. We study the decomposition of these Siegel modular forms in terms of characters of two sub-algebras: one is a sl(2)ˆ and the second is a Borcherds extension of the sl(2)ˆ. This is a continuation of our previous work where we studied the case of Siegel modular forms appearing in the context of Umbral moonshine. This situation is more intricate and provides us with a new example (for N=5) that did not appear in that case. We restrict our analysis to the first N terms in the expansion as a first attempt at deconstructing the Siegel modular forms and unravelling the structure of potentially new Lie algebras that occur for N=5,6.

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      "surname": "Shabbir", 
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      "full_name": "Shabbir, Mohammad", 
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      "title": "Decomposition of denominator formulae of some BKM Lie superalgebras - II"
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      "source": "Elsevier", 
      "value": "The square-root of Siegel modular forms of CHL <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>N</mi></mrow></msub></math> orbifolds of type II compactifications are denominator formulae for some Borcherds-Kac-Moody Lie superalgebras for <math><mi>N</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></math>. We study the decomposition of these Siegel modular forms in terms of characters of two sub-algebras: one is a <math><mover><mrow><mi>s</mi><mi>l</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mo>\u02c6</mo></mrow></mover></math> and the second is a Borcherds extension of the <math><mover><mrow><mi>s</mi><mi>l</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mo>\u02c6</mo></mrow></mover></math>. This is a continuation of our previous work where we studied the case of Siegel modular forms appearing in the context of Umbral moonshine. This situation is more intricate and provides us with a new example (for <math><mi>N</mi><mo>=</mo><mn>5</mn></math>) that did not appear in that case. We restrict our analysis to the first N terms in the expansion as a first attempt at deconstructing the Siegel modular forms and unravelling the structure of potentially new Lie algebras that occur for <math><mi>N</mi><mo>=</mo><mn>5</mn><mo>,</mo><mn>6</mn></math>."
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Published on:
21 February 2023
Publisher:
Elsevier
Published in:
Nuclear Physics B , Volume 989 C (2023)

Article ID: 116127
DOI:
https://doi.org/10.1016/j.nuclphysb.2023.116127
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: