Double-Scaling Limit in the Principal Chiral Model: A New Noncritical String?

Vladimir Kazakov; Evgeny Sobko; Konstantin Zarembo

doi:10.1103/PhysRevLett.124.191602

Double-Scaling Limit in the Principal Chiral Model: A New Noncritical String?

Phys Rev Lett. 2020 May 15;124(19):191602. doi: 10.1103/PhysRevLett.124.191602.

Authors

Vladimir Kazakov¹, Evgeny Sobko², Konstantin Zarembo³

Affiliations

¹ Laboratoire de physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 24 rue Lhomond, 75005 Paris, France and Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland.
² School of Physics and Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.
³ Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen, Denmark, and Hamilton Mathematics Institute, Trinity College Dublin, Dublin 2, Ireland.

PMID: 32469597
DOI: 10.1103/PhysRevLett.124.191602

Abstract

We initiate a systematic, non-perturbative study of the large-N expansion in the two-dimensional SU(N)×SU(N) principal Chiral model (PCM). Starting with the known infinite-N solution for the ground state at fixed chemical potential, we devise an iterative procedure to solve the Bethe ansatz equations order by order in 1/N. The first few orders, which we explicitly compute, reveal a systematic enhancement pattern at strong coupling calling for the near-threshold resummation of the large-N expansion. The resulting double-scaling limit bears striking similarities to the c=1 noncritical string theory and suggests that the double-scaled PCM is dual to a noncritical string with a (2+1)-dimensional target space where an additional dimension emerges dynamically from the SU(N) Dynkin diagram.