Federico Ambrosino

We propose a manifestly supersymmetric formulation of the symmetry topological field theory for theories with supersymmetry. Our construction provides a superspace description in which symmetry and anomaly data, together with the relations among them imposed by supersymmetry, are manifestly organized into supermultiplets. Using the supergeometric formalism, we develop the general framework as a supersymmetric extension of BF theory and illustrate how familiar symmetry data are repackaged within it. As a first application, we study the two-dimensional compact superboson and its chiral counterpart, providing simple examples of the general construction.

A bstract: We develop a general formalism to describe the Renormalization Group Flow of Schur indices and fusion algebras of BPS line defects in four-dimensional 𝒩 = 2 Supersymmetric Quantum Field Theories. The formalism includes and extends known results about the Seiberg-Witten description of these structures. Another application of the formalism is to describe the spectrum of BPS partices of 𝒩 = 2 gauge theories with matter in terms of the spectrum of pure 𝒩 = 2 gauge theories. Applications to the theory of quantum groups and to the quantization of cluster varieties are also discussed.

The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings, we focus on line defects in 2d[ ]QFT and we point out that topological defects naturally embed into a larger class, namely, translation invariant defects. The latter still allow for nonsingular fusion and one obtains a monoidal category of translation invariant defects which contains that of topological defects as a full subcategory. We give a simple perturbative description of translation invariant defects in a perturbed conformal field theory via chiral three-dimensional topological field theory. We show in the example of the Ising CFT and the Lee–Yang CFT that even if no topological defects survive the deformation, some translation invariant defects still do.

The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings we focus on line defects in 2d QFT and we point out that topological defects naturally embed into a larger class, namely translation invariant defects. The latter still allow for non-singular fusion and one obtains a monoidal category of translation invariant defects which contains that of topological defects as a full subcategory. We give a simple perturbative description of translation invariant defects in a perturbed conformal field theory via chiral three-dimensional topological field theory. We show in the example of the Ising CFT and the Lee-Yang CFT that even if no topological defects survive the deformation, some translation invariant defects still do.

We investigate non-local conserved charges in perturbed two-dimensional conformal field theories (CFT) from the point of view of the 3d symmetry TFT (SymTFT) of the unperturbed theory. In the SymTFT we state a simple commutation condition which results in a pair of compatible bulk and defect perturbations, such that the perturbed line defects are conserved in the perturbed CFT. In other words, the perturbed defects are rigidly translation invariant, and such defects form a monoidal category which extends the topological symmetries. As examples we study the A-type Virasoro minimal models M ( p , q ) . Our formalism provides one-parameter families of commuting non-local conserved charges for perturbations by a primary bulk field with Kac label (1, 2), (1, 3), or (1, 5), which are the standard integrable perturbations of minimal models. We find solutions to the commutation condition also for other bulk perturbations, such as (1, 7), and we contrast this with the existence of local conserved charges. There has been recent interest in the possibility that in certain cases perturbations by fields such as (1, 7) can be integrable, and our construction provides a new way in which integrability can be found without the need for local conserved charges.

In this Letter we continue the investigation of RG flows between Virasoro minimal models of two-dimensional conformal field theories that are protected by noninvertible symmetries. RG flows leaving unbroken a subcategory of noninvertible symmetries are associated with anomaly matching conditions that we employ systematically to map the space of flows between minimal models beyond the Z 2 -symmetric proposed recently in the literature. We introduce a family of nonlinear integral equations that appear to encode the exact finite-size, ground-state energies of these flows, including nonintegrable cases, such as the recently proposed M ( k q + I , q ) → M ( k q − I , q ) . Our family of NLIEs encompasses and generalizes the integrable flows known in the literature: ϕ ( 1 , 3 ) , ϕ ( 1 , 5 ) , ϕ ( 1 , 2 ) and ϕ ( 2 , 1 ) . This work uncovers a new interplay between exact solvability and noninvertible symmetries. Furthermore, our nonperturbative description provides a nontrivial test for all the flows conjectured by anomaly matching conditions, but so far not observed by other means.

We study analytic properties and integrable structures of the meson spectrum in large N _c QCD₂. We show that the integral equation that determines the masses of the mesons, often called the ’t Hooft equation, is equivalent to finding solutions to a TQ-Baxter equation. Our analysis extends some of previous results by Fateev et al. to general quark masses m = m ₁ = m ₂, as a perturbative series of the mass parameter. This reformulation, together with its relation to an inhomogeneous Fredholm equation, makes accessible the analytic structure of the spectrum in the complex plane of the quark masses. We also comment on applications of our techniques to non-perturbative topological string partition functions.

We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p -form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a new Stückelberg mechanism to give a mass to free fermionic fields. Furthermore, we find new magnetic fermionic symmetries in these physical systems whose charged objects are disorder operators. For the case of a 4D Dirac spinor, we discuss a dual description, where the magnetic symmetry acts on the holonomies of a dual 2-form tensor-spinor. Further generalizations such as higher-group-like structures are also discussed. Published by the American Physical Society 2024