Combinatorial solution of the eclectic spin chain

Changrim Ahn, Luke Corcoran, Matthias Staudacher

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6 Scopus citations


The one-loop dilatation operator in the holomorphic 3-scalar sector of the dynamical fishnet theory is studied. Due to the non-unitary nature of the underlying field theory this operator, dubbed in [1] the eclectic spin chain Hamiltonian, is non-diagonalisable. The corresponding spectrum of Jordan blocks leads to logarithms in the two-point functions, which is characteristic of logarithmic conformal field theories. It was conjectured in [2] that for certain filling conditions and generic couplings the spectrum of the eclectic model is equivalent to the spectrum of a simpler model, the hypereclectic spin chain. We provide further evidence for this conjecture, and introduce a generating function which fully characterises the Jordan block spectrum of the simplified model. This function is found by purely combinatorial means and is simply related to the q-binomial coefficient.

Original languageEnglish
Article number28
JournalJournal of High Energy Physics
Issue number3
StatePublished - Mar 2022

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