A Proof of Selection Rules for Critical Dense Polymers

Abstract

Among the lattice loop models defined by Pearce, Rasmussen and Zuber (2006), the model corresponding to critical dense polymers ($\beta =0$) is the only one for which an inversion relation for the transfer matrix $D_N(u)$ was found by Pearce and Rasmussen (2007). From this result, they identified the set of possible eigenvalues for $D_N(u)$ and gave a conjecture for the degeneracies of its relevant eigenvalues in the link representation, in the sector with $d$ defects. In this paper, we set out to prove this conjecture, using the homomorphism of the $T{L}_N(\beta )$ algebra between the loop model link representation and that of the XXZ model for $\beta =-(q+q^{-1})$.

39 pages

References in corpus (4)

• Indecomposability parameters in chiral Logarithmic Conformal Field Theory
• Character decomposition of Potts model partition functions. I. Cyclic geometry
• Eigenvalue amplitudes of the Potts model on a torus
• Combinatorial aspects of boundary loop models

Cited by in corpus (12)

• Boundary algebras and Kac modules for logarithmic minimal models
• Modular invariant partition function of critical dense polymers
• Jordan cells of periodic loop models
• Integrability and conformal data of the dimer model
• A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra
• Refined conformal spectra in the dimer model
• Finite-size corrections for logarithmic representations in critical dense polymers
• Conformal partition functions of critical percolation from $D_3$ Thermodynamic Bethe Ansatz equations
• Bipartite fidelity of critical dense polymers
• Two-point boundary correlation functions of dense loop models
• Infinitely extended Kac table of solvable critical dense polymers
• Yang-Baxter Integrable Dimers on a Strip