Tensors, state-sum TFTs and the evaluation of (extruded) graphs

Christoph Schweigert (U Hamburg)

Oct 05. 2022, 10:50 — 12:00

We recall that three-dimensional topological field theories with boundaries
form a natural geometric realization for two-dimensional tensor network
models. The entries of various tensors (PEPS, MPO) arise in the state-sum
construction as evaluations of tetrahedral graphs on spheres. They are thus (mixed) 6j-symbols.

We extend these evaluations of graphs on spheres to include general configurations
of surface defects and bulk Wilson lines. This leads to
an intrinsically three-dimensional calculus, yielding
tensors that still can be computed in terms of traces.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Tensor Networks: Mathematical Structures and Novel Algorithms (Thematic Programme)
Frank Pollmann (TU Munich)
Norbert Schuch (U of Vienna)
Frank Verstraete (Ghent U)