Emergent Physics From Lattice Models of Higher Gauge Theory

A Research Project Grant, funded by the Leverhulme Trust .


Grant period:
  • 1st September 2018 – 31st March 2020, and
  • 1st October 2020 – 31st March 2021.

  • Participants:
  • Dr. João Faria Martins, PI;
  • Prof. Paul Purdon Martin, co-I;
  • Prof. Jiannis Pachos, member of the steering committee;
  • Dr. Celeste Damiani (until March 2020), research fellow funded by the Leverhulme Trust,
  • Dr. Vincent Koppen (from October 2020), research fellow funded by the Leverhulme Trust.


  • Our project aim is to investigate the different types of point-like and loop / string-like topologically excited states arising in higher gauge theory lattice models for (3+1)-dimensional topological phases of matter, categorifying Kitaev quantum double model for (2+1)-dimensional topological phases. A central topic of this project concerns analysing the behaviour of loop excitations when they move in three-dimensional space, braid and interact, and explore applications to topological quantum computing and to knot theory in four dimensions.

    Keywords:

    • TQFTs; • Extended TQFTs; • Knotted Surfaces; • Loop Braid Group and Necklace Braid Group; • 2-group; • Crossed Module; • Higher Gauge Theory; • Categorification; • Topological Quantum Computing; • Braided Fusion Category; • Braided Fusion 2-Category.

    Workshop in Leeds:

    Some talk videos


    Some talk slides


    Publications completed during grant period:


    Publications in final form during grant period:


    Some relevant previous publications