Towards a mathematical conjecture for the Landau-Ginzburg/conformal field theory correspondence and beyond

Samenvatting

The interplay between mathematics and (theoretical) physics has inspired a large amount of research. This proposal focuses on a particular topic in this area called the Landau- Ginzburg/conformal field theory correspondence. This correspondence dates from the late 80s and early 90s in the theoretical physics literature and it relates very different algebraic structures describing on the one hand boundary conditions and defects for Landau–Ginzburg models and N=2 superconformal field theories on the other. Thanks to very recent developments in both the theory of Landau-Ginzburg models and mathematical descriptions of conformal field theories (leading to some first examples of this correspondence), we have all the necessary tools for pushing forward our mathematical understanding of this correspondence.
The aim of this project is to provide a mathematical statement for the Landau–Ginzburg/ conformal field theory correspondence. For this, first I will complete a classification of examples and explore their properties, which will reveal how a conjecture will look like. This research will involve techniques of representation theory, quantum algebra and category theory. Once this task is achieved, I will embed all these results into a precise conjecture using higher categorical methods. The final stage of this project is to prove this conjecture, and explore further extensions of these results beyond the N=2 superconformal field theories.

Kenmerken

Projectnummer

639.031.758

Hoofdaanvrager

Dr. A. Ros Camacho

Verbonden aan

Universiteit Utrecht

Looptijd

01/09/2017 tot 31/08/2020