RG Limit Cycles in BKT Flows ≡ Periodic Real-Time Dynamics in the Current-Current Perturbed SU(2)1 WZW Model
Abstract
We establish an exact correspondence between renormalization-group (RG) evolution and real-time quantum dynamics in the anisotropic current-current perturbed SU(2)1 Wess-Zumino-Witten (WZW) model. Using its integrable fermionic representation, we construct the exact time-dependent many-body wavefunction by means of the generalized Bethe ansatz and show that periodic boundary conditions lead to quantum Knizhnik-Zamolodchikov equations associated with the XXZ trigonometric R-matrix, which corresponds to the quantum affine algebra 𝒰q(sl2̂) evaluated in its spin-1/2 evaluation representation. Consistency of these equations constrains the temporal evolution of the longitudinal and transverse interaction strengths. In the universal regime, these integrability conditions are exactly equivalent to the Berezinskii-Kosterlitz-Thouless RG flow equations upon identifying physical time with the logarithmic RG scale. Consequently, the RG limit cycles of the anisotropic current-current perturbed SU(2)1 WZW model are realized as periodic real-time evolution of its interaction strengths. Our results provide an exact dynamical realization of RG limit cycles and establish a direct connection between cyclic RG flows, quantum integrability, and periodically driven interacting quantum field theories.
Related
- Heteroclinic cycles and long-time behavior in a singularly perturbed three-species Lotka--Volterra system
- Functional limit theorems for perturbed random walks
- THE HYDRODYNAMIC LIMIT FOR THE ENERGY TRANSPORT IN A STOCHASTICALLY PERTURBED HARMONIC CHAIN OF OSCILLATORS
- Bifurcation of limit cycles in piecewise holomorphic systems separated by two external circles
- Conley Index of Limit Cycles in Filippov Vector Fields
BibTeX
@misc{pasnoori2026limit,
title = {{RG Limit Cycles in BKT Flows $\equiv$ Periodic Real-Time Dynamics in the Current-Current Perturbed $SU(2)_1$ WZW Model}},
author = {Parameshwar R. Pasnoori},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34248},
eprint = {2609.34248},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34248},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - RG Limit Cycles in BKT Flows ≡ Periodic Real-Time Dynamics in the Current-Current Perturbed SU(2)_1 WZW Model
AU - Parameshwar R. Pasnoori
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34248
UR - https://arxiv.org/abs/2609.34248
AB - We establish an exact correspondence between renormalization-group (RG) evolution and real-time quantum dynamics in the anisotropic current-current perturbed SU(2)_1 Wess-Zumino-Witten (WZW) model. Using its integrable fermionic representation, we construct the exact time-dependent many-body wavefunction by means of the generalized Bethe ansatz and show that periodic boundary conditions lead to quantum Knizhnik-Zamolodchikov equations associated with the XXZ trigonometric R-matrix, which corresponds to the quantum affine algebra 𝒰_q(sl_2̂) evaluated in its spin-1/2 evaluation representation. Consistency of these equations constrains the temporal evolution of the longitudinal and transverse interaction strengths. In the universal regime, these integrability conditions are exactly equivalent to the Berezinskii-Kosterlitz-Thouless RG flow equations upon identifying physical time with the logarithmic RG scale. Consequently, the RG limit cycles of the anisotropic current-current perturbed SU(2)_1 WZW model are realized as periodic real-time evolution of its interaction strengths. Our results provide an exact dynamical realization of RG limit cycles and establish a direct connection between cyclic RG flows, quantum integrability, and periodically driven interacting quantum field theories.
ER -