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<p>The Moonshine module is a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(c=24\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo>=</mo> <mn>24</mn> </mrow> </math></EquationSource> </InlineEquation> conformal field theory (CFT) whose automorphism group is the Monster group. It was argued by Dixon, Ginsparg, and Harvey in Dixon et al. (Commun Math Phys 119:221–241, 1988. <a href="https://doi.org/10.1007/BF01217740">https://doi.org/10.1007/BF01217740</a>) that there exists a spin lift of the Moonshine CFT with superconformal symmetry. Reference Dixon et al. (1988) did not provide an explicit construction of a superconformal current. The present paper provides an explicit construction of a supercurrent. In fact, we will construct several superconformal currents in a spin lift of the Moonshine CFT using techniques developed in Harvey and Moore (JHEP 05:146, 2020. <a href="https://doi.org/10.1007/JHEP05(2020)146">https://doi.org/10.1007/JHEP05(2020)146</a>. <a href="http://arxiv.org/abs/2003.13700">arXiv:2003.13700</a> [hep-th]). In particular, our construction relies on error correcting codes.</p>

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Beauty and the Beast Part 2: Apprehending the Missing Supercurrent

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  • 发表日期：

    2025年10月30日

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  • Gregory W. Moore,
  • Ranveer Kumar Singh

摘要

The Moonshine module is a \(c=24\) c = 24 conformal field theory (CFT) whose automorphism group is the Monster group. It was argued by Dixon, Ginsparg, and Harvey in Dixon et al. (Commun Math Phys 119:221–241, 1988. https://doi.org/10.1007/BF01217740) that there exists a spin lift of the Moonshine CFT with superconformal symmetry. Reference Dixon et al. (1988) did not provide an explicit construction of a superconformal current. The present paper provides an explicit construction of a supercurrent. In fact, we will construct several superconformal currents in a spin lift of the Moonshine CFT using techniques developed in Harvey and Moore (JHEP 05:146, 2020. https://doi.org/10.1007/JHEP05(2020)146. arXiv:2003.13700 [hep-th]). In particular, our construction relies on error correcting codes.