# Prof. Dr. Katrin Wendland

**Source**: https://www.maths.tcd.ie/~wendland/projects/phd.html
**Parent**: https://www.maths.tcd.ie/~wendland/research.html

In the framework of my Ph.D. project, jointly with
[Prof. Werner Nahm](http://www.stp.dias.ie/TPPG/tppg.html) we
investigated the moduli space M of N=(4,4)
superconformal field theories (SCFTs) with central charge c=6.

Our results can be found in

Werner Nahm, Katrin Wendland

A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with Central Charge c=6

- [Commun. Math. Phys. **216** (2001), 85-138](http://link.springer.com/article/10.1007/PL00005548)
- [hep-th/9912067](http://de.arXiv.org/abs/hep-th/9912067)

After a slight emendation of the previously known global description of M, we find the locations of various known models in the
component MK3 associated to K3 surfaces.
Among them are the Z2 and Z4 orbifold theories obtained
from the torus component of M. Here, SO(4,4)
triality is found to play a crucial role. Using our embedding of the space of
Z2 orbifold theories in MK3,
we give a direct proof for a widely spread but previously unproved statement
about the behavior of the B-field under the orbifold procedure. We prove
T-duality for Z2 orbifolds and use it to derive the form of M purely within conformal field theory, thus completing the final step in the
proof of the form of M which was left open in the literature,
previously.

Restricting to the bosonic parts of the theories, we also find two meeting
points of Mtori and MK3, generalizing results by Kobayashi and
Sakamoto. We correct and prove a conjecture by Eguchi, Ooguri, Taormina and
Yang on possible meeting points of the moduli spaces of Z2 and
Z4 orbifold CFTs. We moreover prove isomorphies of specific
examples of orbifold CFTs to so-called Gepner and Gepner type models, one of
which had been conjectured before by Eguchi, Ooguri, Taormina and Yang. This
enables us to give the precise location of these models in the moduli space, in
particular to prove the long standing and widely used conjecture that the
Gepner model (2)4 admits a geometric interpretation on the Fermat
quartic hypersurface. [Later](https://www.maths.tcd.ie/~wendland/projects/postdoc.html "Attractive
Quartics"), I have clarified and extended the latter result, showing
how on every "very attractive" quartic X a SCFT can be constructed explicitly.

With Sayipjamal Dulat I have made a contribution to the classification
of two dimensional conformal field theories with central charge c=2:

Sayipjamal Dulat, Katrin Wendland

Crystallographic Orbifolds: Towards a Classification of Unitary Conformal Field Theories with Central Charge c=2

- JHEP **0006**:012 (2000)
- [hep-th/0002227](http://de.arXiv.org/abs/hep-th/0002227)

We construct all the 26 non-exceptional non-isolated irreducible components of
the moduli space of such theories that may be obtained by an orbifold procedure
from toroidal ones, their parameter spaces, and their partition functions. The
global structure of this part of the moduli space follows from our
determination of all multicritical points and lines. The results of Dixon,
Ginsparg and Harvey on the classification of superconformal theories (SCFTs)
with central charge c=3/2 serve as a cross check. In particular, all their
non-isolated orbifolds as well as orbifolds with discrete torsion gain
geometric interpretations due to our results.

In my Ph.D. thesis, I had also corrected the claims made in Dixon, Ginsparg and
Harvey on multicritical points among the orbifolds with central charge c=3/2.
This discussion as well as the general construction and classification of all
so-called superaffine, orbifold prime and super-M-orbifold models in arbitrary
dimensions is given in my later publication

Katrin Wendland

Superconformal orbifolds involving the fermion number operator

- [Int. J. Mod. Phys. A. Vol. **19** (2004), 3637-3667](http://www.worldscinet.com/ijmpa/19/1922/S0217751X04019779.html)

\
\
\