TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.14.3.043
TI  - Dynamically restoring conformal invariance in (integrable) $\sigma$-models
PY  - 2023/03/21
UR  - https://scipost.org/SciPostPhys.14.3.043
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 14
IS  - 3
SP  - 043
A1  - Aliaj, Rigers
AU  - Sfetsos, Konstantinos
AU  - Siampos, Konstantinos
AB  - Integrable $\lambda$-deformed $\sigma$-models are characterized by an underlying current algebra/coset model CFT deformed, at the infinitesimal level, by current/parafermion bilinears. We promote the deformation parameters to dynamical functions of time introduced as an extra coordinate. It is conceivable that by appropriately constraining them, the beta-functions vanish and consequently the $\sigma$-model stays conformal. Remarkably, we explicitly materialize this scenario in several cases having a single and even multiple deformation parameters. These generically obey a system of non-linear second-order ordinary differential equations. They are solved by the fixed points of the RG flow of the original $\sigma$-model. Moreover, by appropriately choosing initial conditions we may even interpolate between the RG fixed points as the time varies from the far past to the far future. Finally, we present an extension of our analysis to the Yang--Baxter deformed PCMs.
ER  -

@Article{10.21468/SciPostPhys.14.3.043,
	title={{Dynamically restoring conformal invariance in (integrable) $\sigma$-models}},
	author={Rigers Aliaj and Konstantinos Sfetsos and Konstantinos Siampos},
	journal={SciPost Phys.},
	volume={14},
	pages={043},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.14.3.043},
	url={https://scipost.org/10.21468/SciPostPhys.14.3.043},
}