Year: 2019
Type: article
Abstract: The existence of higher-spin quantum conserved currents in two dimensions guarantees quantum integrability.We revisit the question [1] of whether classically-conserved local higher-spin currents in two-dimensional sigma models survive quantization.We define an integrability index IpJq for each spin J, with the property that IpJq is a lower bound on the number of quantum conserved currents of spin J.In particular, a positive value for the index establishes the existence of quantum conserved currents.For a general coset model, with or without extra discrete symmetries, we derive an explicit formula for a generating function that encodes the indices for all spins.We apply our techniques to the N´1 model, the OpNq model, and the flag sigma model UpNq Up1q N .For the OpNq model, we establish the existence of a spin-6 quantum conserved current, in addition to the well-known spin-4 current.The indices for the N´1 model for N ą 2 are all non-positive, consistent with the fact that these models are not integrable.The indices for the flag sigma model UpNq Up1q N for N ą 2 are all negative.Thus, it is unlikely that the flag sigma models are integrable.
Source: SciPost Physics
Authors: Shota Komatsu, Raghu Mahajan, Shu-Heng Shao
Institutions: Princeton University, Institute for Advanced Study
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2956977005