Riccardo Argurio, Andrés Collinucci, Giovanni Galati, Ondrej Hulik, Elise Paznokas
SciPost Phys. 18, 089 (2025) ·
published 11 March 2025
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We extend the construction of the T-duality symmetry for the 2d compact boson to arbitrary values of the radius by including topological manipulations such as gauging continuous symmetries with flat connections. We show that the entire circle branch of the $c=1$ conformal manifold can be generated using these manipulations, resulting in a non-invertible T-duality symmetry when the gauging sends the radius to its inverse value. Using the recently proposed symmetry TFT describing continuous global symmetries of the boundary theory, we identify the topological operator corresponding to these new T-duality symmetries as an open condensation defect of the bulk theory, constructed by (higher) gauging an $\mathbb{R}$ subgroup of the bulk global symmetries. Notably, when the boundary theory is the compact boson with a rational square radius, this operator reduces to the familiar T-duality defect described by a Tambara-Yamagami fusion category. This construction thus naturally includes all possible discrete T-duality symmetries of the theory in a unified way.
Andrea Antinucci, Giovanni Galati, Giovanni Rizi, Marco Serone
SciPost Phys. 15, 125 (2023) ·
published 29 September 2023
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We study Ward identities and selection rules for local correlators in disordered theories where a 0-form global symmetry of a QFT is explicitly broken by a random coupling $h$ but it re-emerges after quenched average. We consider $h$ space-dependent or constant. In both cases we construct the symmetry operator implementing the group action, topological after average. In the first case, relevant in statistical systems with random impurities, such symmetries can be coupled to external backgrounds and can be gauged, like ordinary symmetries in QFTs. We also determine exotic selection rules arising when symmetries emerge after average in the IR, explaining the origin of LogCFTs from symmetry considerations. In the second case, relevant in AdS/CFT to describe the dual boundary theory of certain bulk gravitational theories, the charge operator is not purely codimension-1, it can be defined only on homologically trivial cycles and on connected spaces. Selection rules for average correlators exist, yet such symmetries cannot be coupled to background gauge fields in ordinary ways and cannot be gauged. When the space is disconnected, in each connected component charge violation occurs, as expected from Euclidean wormholes in the bulk theory. Our findings show the obstruction to interpret symmetries emergent after average as gauged in the bulk.
