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Finding The Golay Code In A K3 Sigma-Model

December 3, 2018 - 2:00pm to 4:00pm
Varian Physics - Room 355

Professor Greg Moore of Rutgers University will give the Stanford Institute for Theoretical Physics (SITP) Monday Colloquium.

Abstract: The Mathieu Moonshine phenomenon, discovered by Eguchi, Ooguri, and Tachikawa in 2010 has, amazingly, remained a mystery despite concerted efforts to find a conceptual explanation. After reviewing this phenomenon I will review the Quantum Mukai Theorem of Gaberdiel, Hohenegger, and Volpato (GHV). This theorem lists the possible symmetry groups of K3 sigma models. Following ideas developed with Jeff Harvey I will indicate how the GHV groups are easily understood in the context of heterotic/typeII duality. I will then review work of Gaberdiel, Taormina, Volpato, and Wendland (GTVW) showing that the biggest of the GHV groups is realized by a Z_2- orbifold of the Cartan torus of Spin(8). Remarkably, this GTVW conformal field theory is isomorphic to the product of six _bosonic_ SU(2) level k=1 WZW models! I will then describe on-going work with Jeff Harvey: The supercurrents in the SU(2)^6 WZW model are not obvious, and are governed by a quantum code, which turns out to be closely related to the CSS code determined by the classical hexacode. Since the EOT observation really only requires (4,1) supersymmetry we are motivated to study the symmetry groups of the GTVW model that preserve (4,1) supersymmetry. I will describe our - as yet imperfect - knowledge about this symmetry group and explain that, when acting on the RR sector in a distinguished basis in the SU(2)^6 WZW model the Golay code emerges in the form presented by the Curtis-Conway Miracle Octad Generator.

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Stanford Institute for Theoretical Physics
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