TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.1.033
TI  - Critical spin chains and loop models with $PSU(n)$ symmetry
PY  - 2025/01/27
UR  - https://scipost.org/SciPostPhys.18.1.033
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 1
SP  - 033
A1  - Roux, Paul
AU  - Jacobsen, Jesper Lykke
AU  - Ribault, Sylvain
AU  - Saleur, Hubert
AB  - Starting with the Ising model, statistical models with global symmetries provide fruitful approaches to interesting physical systems, for example percolation or polymers. These include the $O(n)$ model (symmetry group $O(n)$) and the Potts model (symmetry group $S_Q$). Both models make sense for $n,Q∈ \mathbb{C}$ and not just $n,Q∈ \mathbb{N}$, and both give rise to a conformal field theory in the critical limit. Here, we study similar models based on the group $PSU(n)$. We focus on the two-dimensional case, where the models can be described either as gases of non-intersecting orientable loops, or as alternating spin chains. This allows us to determine their spectra either by computing a twisted torus partition function, or by studying representations of the walled Brauer algebra. In the critical limit, our models give rise to a CFT that exists for any $n∈\mathbb{C}$ and has a global $PSU(n)$ symmetry. Its spectrum is similar to those of the $O(n)$ and Potts CFTs, but a bit simpler. We conjecture that the $O(n)$ CFT is a $\mathbb{Z}_2$ orbifold of the $PSU(n)$ CFT, where $\mathbb{Z}_2$ acts as complex conjugation.
ER  -

@Article{10.21468/SciPostPhys.18.1.033,
	title={{Critical spin chains and loop models with $PSU(n)$ symmetry}},
	author={Paul Roux and Jesper Lykke Jacobsen and Sylvain Ribault and Hubert Saleur},
	journal={SciPost Phys.},
	volume={18},
	pages={033},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.1.033},
	url={https://scipost.org/10.21468/SciPostPhys.18.1.033},
}