TY - JOUR
T1 - Combinatorial solution of the eclectic spin chain
AU - Ahn, Changrim
AU - Corcoran, Luke
AU - Staudacher, Matthias
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/3
Y1 - 2022/3
N2 - 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.
AB - 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.
KW - AdS-CFT Correspondence
KW - Integrable Field Theories
KW - Lattice Integrable Models
UR - http://www.scopus.com/inward/record.url?scp=85126198392&partnerID=8YFLogxK
U2 - 10.1007/JHEP03(2022)028
DO - 10.1007/JHEP03(2022)028
M3 - Article
AN - SCOPUS:85126198392
SN - 1126-6708
VL - 2022
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 3
M1 - 28
ER -