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Title:
The W3 algebra: unitarity and strong locality outside the comfort zone
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Abstract:
Both vertex operator algebras (VOAs) and conformal (Haag-Kastler) nets of von Neumann algebras were introduced as mathematical formalizations of conformal quantum field theory. However, the passage from one to the other is often challenging. In particular, strating from a VOA, in order to obtain a conformal net, one needs to show the existence of a unitary structure and the strong locality of the fields. For affine VOAs unitarity is simple to check by costruction and strong locality follows because currents satisfy linear energy bounds. Also, many other VOAs can be dealt with by finding suitable (unitarity preserving) embeddings into affine VOAs. However, VOAs with no known such embeddings and also with no linear energy bounds are much harder to treat; in many sense they are outside the "comfort zone". I will talk about an interesting case study regarding the W3 algebra. It is perhaps the simplest VOA which is NOT generated by dimension 1 and 2 fields (i.e. by fields that can possibly satisfy linear energy bounds). That is, the simplest VOA outside the comfort zone
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