Limiting processes for CFTs

The main results of my work with Dr. Daniel Roggenkamp are contained in the publications

Daniel Roggenkamp, Katrin Wendland
Limits and Degenerations of Unitary Conformal Field Theories
Katrin Wendland (joint work with Daniel Roggenkamp)
On degenerating sequences of CFTs and their geometric interpretations
  • Oberwolfach Report No. 24/2004 (2004), pp. 1301-1302


Daniel Roggenkamp, Katrin Wendland
Decoding the geometry of conformal field theories

We investigate degeneration phenomena in families of conformal field theories and establish an intrinsic notion of limiting processes for unitary CFTs as well as degenerate limits. We show that our definition allows to associate a geometric intepretation to each degenerate limit, ensuring that it carries a structure similar to that predicted by Kontsevich and Soibelman in the context of mirror symmetry on tori. We prove that our techniques apply to the sequence of diagonal unitary Virasoro minimal models in the large level limit. In particular, this sequence converges and degenerates according to our definitions, and we find a geometric interpretation for its limit, including the metric, the dilaton, and the D-brane geometry on the target space. This rather technical work is the starting point for various further investigations which should lead to an intrinsic conceptual understanding of the geometry encoded in CFTs, including the boundary sector.

The second publication contains a less technical summary of the original paper, as well as the proof of an identity known as "seven term identity" for our limiting CFTs. This allows us to interpret the limiting zero mode of the total Virasoro field as a Laplace type operator in a degenerate limit of CFTs, a property which previously had to be assumed separately.