Giovanni Rizi

We consider the dynamics of confined strings embedded in a gapless four-dimensional theory. To this end, we examine finite-tension string-like solutions to the equations of motion of the \mathbb{C}\mathbb{P}^1 ℂ ℙ 1 non-linear sigma model. We present a comprehensive analysis of the quantum fluctuations around these solutions and derive the corresponding spectrum. These results allow us to determine the quantum corrections to the closed string ground state energy in both the finite- and infinite-size limits. Furthermore, we analyze quantum corrections to the string’s effective width. We find that these observables generically depart from the universal predictions of standard Effective String Theory (EST), and we identify specific limits in which the bulk dynamics decouple and EST is recovered. We find that the leading corrections beyond the EST regime scale logarithmically with the string length, providing a smoking gun of the interactions with a gapless bulk. Finally, we discuss the connection between these string configurations and stable electric and magnetic fluxes arising in certain ultraviolet completions of the \mathbb{C}\mathbb{P}^1 ℂ ℙ 1 model.

We explore a general mechanism that allows ( 1 + 1 ) d CFTs to have interesting interface conformal manifolds even in the absence of any continuous internal symmetry or supersymmetry. This is made possible by the breaking of an enhanced continuous symmetry—which is generically noninvertible—arising in the folded theory. We provide several examples and showcase the power of the symmetry-based approach by computing the evolution of the reflection coefficient along the defect conformal manifold. We also discuss higher-dimensional generalizations and we comment on no-go theorems.

A bstract: We construct examples of non-invertible global symmetries in two-dimensional superconformal field theories described by sigma models into Calabi-Yau target spaces. Our construction provides some of the first examples of non-invertible symmetry in irrational conformal field theories. Our approach begins at a Gepner point in the conformal manifold where the sigma model specializes to a rational conformal field theory and we can identify all supersymmetric topological Verlinde lines. By deforming away from this special locus using exactly marginal operators, we then identify submanifolds in moduli space where some non-invertible symmetry persists. For instance, along ten-dimensional loci in the complex structure moduli space of quintic Calabi-Yau threefolds there is a symmetry characterized by a Fibonacci fusion category. The symmetries we identify provide new constraints on spectra and correlation functions. As an application we show how they constrain conformal perturbation theory, consistent with recent results about scaling dimensions in the K3 sigma model near its Gepner point.

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 h but it re-emerges after quenched average. We consider h 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.