PIRSA:26050039 Scientific Series Quantum Fields and Strings

DOI10.48660/26050039

Series: Quantum Fields and Strings

Gorantla, P. (2026). Non-invertible symmetries on the lattice. Perimeter Institute. https://pirsa.org/26050039

Gorantla, Pranay. Non-invertible symmetries on the lattice. Perimeter Institute, May. 12, 2026, https://pirsa.org/26050039 

@misc{ pirsa_PIRSA:26050039,
  doi = {10.48660/26050039},
  url = {https://pirsa.org/26050039},
  author = {Gorantla, Pranay},
  keywords = {Quantum Fields and Strings},
  language = {en},
  title = {Non-invertible symmetries on the lattice},
  publisher = {Perimeter Institute},
  year = {2026},
  month = {may},
  note = {PIRSA:26050039 see, \url{https://pirsa.org}}
}

Abstract

Non-invertible symmetries have received a lot of attention in the last few years, with nontrivial applications in both high energy physics and condensed matter physics. I will discuss exact realizations of non-invertible symmetries on the lattice. Specifically, I will present a tensor network representation of non-invertible duality symmetries, such as the well known Kramers-Wannier duality in 1+1d and the Wegner duality in 3+1d, using a graphical tool from quantum information known as ZX-calculus. I will then discuss some low energy consequences of these symmetries in explicit lattice models. In particular, I will introduce a deformation of the 3+1d lattice Z2 gauge theory with exactly degenerate and (provably) gapped ground states, which include a product state and the toric code ground states. I’ll end with some generalisations and future directions.

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