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Moonshine Anomalies

Mathematical Physics Seminar

Speaker: Theo Johnson-Freyd, Perimeter Institute
Location: 2112 MSB
Start time: Fri, Feb 9 2018, 11:00AM

Many sporadic groups G admit distinguished "moonshine" representations on conformal field theories --- the original and most famous example being the "defining" representation of the Monster group. Any such action produces an accompanying gauge anomaly living in H^4(G;Z). I will discuss the values of these anomalies, and suggest that often the anomaly of the distinguished "moonshine" action generates the corresponding cohomology group. In particular, I will report on my calculation, joint with David Treumann, of the fourth cohomology of the largest Conway group and of the O'Nan group, and on my calculation of the order of the Monster's moonshine anomaly. The latter calculation uses a construction I call "finite group T-duality" which may be of independent interest.