Exploring duality symmetries, multicriticality and RG flows at $c = 2$

TL;DR

This paper investigates non-invertible duality symmetries in the $c=2$ conformal manifold, analyzing their construction, categorical data, and impact on RG flows, especially at multicritical points where orbifold branches intersect.

Contribution

It provides a systematic method to construct symmetry defects for rational CFTs at $c=2$, and explores their role in multicritical theories and RG flows, revealing new insights into duality symmetries.

Findings

All rational CFTs along the $c=2$ branch have duality symmetries.

Categorical data and defect Hilbert spaces are derived for multicritical examples.

Non-invertible symmetries constrain IR behavior in RG flows.

Abstract

In this work, we study the realization of non-invertible duality symmetries along the toroidal branch of the $c=2$ conformal manifold. A systematic procedure to construct symmetry defects is implemented to show that all Rational Conformal Field Theories along this branch enjoy duality symmetries. Furthermore, we delve into an in-depth analysis of two representative cases of multicritical theories, were the toroidal branch meets various orbifold branches. For these particular examples, the categorical data and the defect Hilbert spaces associated to the duality symmetries are obtained by resorting to modular covariance. Finally, we study the interplay between these novel symmetries and the various exactly marginal and relevant deformations, including some representative examples of Renormalization Group flows where the infrared is constrained by the non-invertible symmetries and their anomalies.