A Deformed, Integrable, Non-Diagonalizable Spin Chain from QFT

Abstract: I discuss the features of certain integrable spin chains one obtains from the dilatation operator of strongly twisted, double-scaled deformations of $\mathcal{N} = 4$ Super Yang-Mills Theory. A particular case is a certain chiral three-state model with an exceedingly simple Hamiltonian. It is non-diagonalizable, and shows very rich and intricate patterns of Jordan cell formation. I explain some of the difficulties one faces when applying the quantum inverse scattering method to these models. I also sketch how to find a beautiful solution to this problem. Finally, I will briefly discuss some relations to logarithmic four-dimensional quantum field theories and in particular the resulting challenges for a complete understanding of fishnet-type models.

HEP - theory

Audience: researchers in the topic

Exact Results on Irrelevant Deformations of QFTs

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