Flandoli, Ilaria (2017) logarithmic conformal field theories of type Bn; p = 2 and symplectic fermions. [Magistrali biennali]
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In the first part, I present a well-known algebraic object, a *vertex operator algebra* (VOA) *V* associated to a given lattice. I describe its representation theory and define some maps acting on it, called *screening operators*. The established program by B. Feigin et. al. to which my master project contributes asks to consider a sub lattice VOA *W* of *V*, by taking the intersection of the kernels of some screenings. Many conjectures were made in the past years about this new object *W*. In particular it was conjectured that this is a *Logarithmic Conformal Field Theory* (LCFT), i.e. a VOA with a finite but non-semisimple representation theory. Not many LCFT are nowadays known, and the program outlined above has only been completed for rank 1 so far. My master project is to study and completely understand a new example of this construction, where the lattice is a Lie algebra root lattice of type B_n, rescaled by p=2. In the second part I indeed calculate and discuss the screening operators, the representations of *W*, their decomposition behaviour and their graded characters. In the third part I prove that *W* is isomorphic to a known LCFT, the *Symplectic Fermions* VOA. In particular this implies that our *W* is in this case a LCFT. This is hence the first higher rank example, where the program has been successfully completed.
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