BSc defense by Anders Heide Wallberg

Transformation Formulae for the MPS Overlap in dCFT

This thesis first lays out why Matrix Product State overlaps are relevant in dCFT. The QQ-relations and fermionic and bosonic transformations are then presented, with particular focus on the fermionic transformation of the distinguished choice of Dynkin diagram for su(2|1). The overlaps are then reformulated in terms of a superdeterminant of the Gaudin matrix.

A formula for how the superdeterminant transforms under the fermionic transformation on su(2|1) is then presented and proven, though one pole remains to be analyzed further. The result is subsequently generalised to any auxiliary fermionic node for any symmetry algebra su(n|m) and compared to previously found numerical solutions. Transformation formulae for any other Dynkin diagrams are also conjectured, but no proofs are given.

Vejleder: Charlotte Kristjansen
Censor: Marta Orselli

Zoom link: https://ucph-ku.zoom.us/j/69873058985