Three-tier CFTs: Construction from Frobenius algebras.

31 January 2012
Andre Henriques
There is a beautiful classification of full (rational) CFT due to Fuchs, Runkel and Schweigert. The classification says roughly the following. Fix a chiral algebra A (= vertex algebra). Then the set of full CFT whose left and right chiral algebras agree with A is classified by Frobenius algebras internal to Rep(A). A famous example to which one can successfully apply this is the case when the chiral algebra A is affine su(2): in that case, the Frobenius algebras in Rep(A) are classified by A_n, D_n, E_6, E_7, E_8, and so are the corresponding CFTs. Recently, Kapustin and Saulina gave a conceptual interpretation of the FRS classification in terms of 3-dimentional Chern-Simons theory with defects. Those defects are also given by Frobenius algebras in Rep(A). Inspired by the proposal of Kapustin and Saulina, we will (partially) construct the three-tier CFT associated to a given Frobenius algebra.
  • Algebraic and Symplectic Geometry Seminar