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Dynamically restoring conformal invariance in (integrable) $σ$-models

by Rigers Aliaj, Konstantinos Sfetsos, Konstantinos Siampos

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Submission summary

Authors (as registered SciPost users): Konstantinos Siampos
Submission information
Preprint Link: scipost_202210_00030v2  (pdf)
Date accepted: 2022-12-01
Date submitted: 2022-11-02 13:20
Submitted by: Siampos, Konstantinos
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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.

Author comments upon resubmission

Issue 1: The seed models were chosen as an illustration of the method due to their simplicity (been integrable was an additional feature). Note that the dynamically promoted models are not expected to be classically integrable since demanding conformality introduces an additional one-loop factor that is the dilaton, i.e. $\dot\Phi_0(t)=h(t)$.

We have added the following related comment in the conclusion (page 28):

"Two comments are in order concerning ... of the aforementioned dynamical models."

Issue 2: The models in Sections 5.2 (generic semi-simple group) and 6 (non-symmetric coset) address to cases beyond rank-1 and symmetric cosets.

We have added the following related comment in the conclusion (page 28):

"Secondly, although we focused for ... semisimple groups."

and a comment at the end of page 34 - after equation (A.25)

"We have explicitly worked out ... we will not present them here."

Issue 3: We have added a related comment in the restoration of conformality of a generic string background (G,B,\Phi) in the last paragraph of the conclusion (page 29):

"Finally, it would be worth extending ... parameters (the analogues~\eqref{eq7.1} and~\eqref{eq7.2})."

Published as SciPost Phys. 14, 043 (2023)

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