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Lie Groups Quantum Mathematics Seminar

A Cyclic Orbifold Theory for Holomorphic VOAs and Applications

Location:  Hill 705
Date & time: Friday, 23 September 2016 at 12:00PM -

Sven Möller, Technische Universität Darmstadt

 

"A Cyclic Orbifold Theory for Holomorphic VOAs and Applications"

Time: 12:00 PM
Location: Hill 705
Abstract: We develop an orbifold theory for a finite, cyclic group G acting on a suitably regular, holomorphic VOA V. To this end we describe the fusion algebra of the fixed-point VOA V^G and show that V^G has group-like fusion. Then we solve the extension problem for VOAs with group-like fusion. We also show that Schellekens' classification of V_1-structures of "meromorphic conformal field theories" of central charge 24 is a theorem on VOAs.

Finally, we use these results to construct some new holomorphic VOAs of central charge 24 as lattice orbifolds. Together with the work of other authors we arrive at a complete classification of the V_1-structures of suitably regular, holomorphic VOAs of central charge 24.

Moreover, some progress towards a classification of these VOAs themselves has been made recently by us and others.

This is joint work with Nils Scheithauer (Darmstadt) and Jethro van Ekeren (IMPA, Rio de Janeiro) and is partly based on my Ph.D. thesis.

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